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Trigonometry

Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )Trigonometry

Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ )Trigonometry

Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )Trigonometry

ASTC rule in trigonometry (Still Confused?

Try reviewing these fundamentals first

Trigonometry

Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )Trigonometry

Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ )Trigonometry

Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )Trigonometry

ASTC rule in trigonometry (Nope, got it.

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- Lesson: 22:20

When you hear SohCahToa, it may sound like a different language entirely. But it's actually an easier way for you to remember how to use sine, cosine and tangent. These three are the main functions that you'll deal with in trigonometry problems.

SohCahToa stands for:

It can help you find the length of a side of a right triangle as long as you have an angle $\theta$ and some info on the other sides of the triangle.

Yes, SohCahToa is only for right triangles. That's because only right triangles have a hypotenuse. Depending on which angle (whichever angle it is, it's called the angle $\theta$) you're using, you'd then figure out what the opposite or the adjacent is.

The adjacent side is always next to the angle. It's the side next to the angle that is not the hypotenuse. The opposite side is simply the side that's opposite of the angle.

Once you have several of the components given to you in a question, you'll be able to figure out unknowns that aren't given! You should also review how to find hypotenuse before we proceed. We'll try a question below to put Soh Cah Toa into use.

**Question 1: **

Find the length of $\overline{BC}$

**Solution:**

$\triangle$ABD is a right angle triangle by itself. This means we can look for $\overline{AB}$ using tan. Tan takes the opposite over the hypotenuse (Toa in SohCahToa).

$\tan 22$° $= \frac{\overline{AB}}{80}$

$\overline{AB}= 32.3 cm$

Now that we've got $\overline{AB}$, we can look for $\overline{AC}$ using tan. $\triangle$ACD is also a right angle triangle, so we can use SohCahToa. Again, we're making use of Toa in SohCahToa.

$\tan 37$° $= \frac{\overline{AC}}{80}$

$\overline{AC}= 60.3 cm$

We know the lengths of $\overline{AB}$ and $\overline{AC}$, which means we can subtract the length of $\overline{AB}$ from $\overline{AC}$ in order to just get the length of $\overline{BC}$.

$\overline{BC} =$ $\overline{AC} -$ $\overline{AB}$

$\overline{BC} = 60.3-32.3$

= 28 cm

A lot of the questions you'll be given require you to put to use several of the trig ratios. You'll always be working with right triangles, so make sure to keep a note of that when you start the question. For example, this question seemed to require you to use $\triangle$BCD at first, but you know that can't be right because it is not a right triangle. Without that 90 degree right angle, you won't be able to use SohCahToa to help you find the unknowns.

Always base your answers around the right triangles in the question and you'll be able to find the answer.

Up for a challenge? Try out this online math test to see if you can answer these trigonometry questions quizzing you on Soh Cah Toa.

A lesson to review that deals with sine, cosine, and tangent includes the ASTC rule. You can also look into these lessons that covers how to find unknowns using the law of sines and the law of cosines. Studying how to find exact values of trigonometric ratios and trig ratios of angles in radians will also advance you further in trig problems

10.

Trigonometry

10.1

Converting between degrees and radians

10.2

Radian measure and arc length

10.3

Angle in standard position

10.4

Coterminal angles

10.5

Reference angle

10.6

Find the exact value of trigonometric ratios

10.7

ASTC rule in trigonometry (All Students Take Calculus)

10.8

Unit circle

10.9

Trigonometric ratios for angles in radians

10.10

Solving first degree trigonometric equations

10.11

Determining non-permissible values for trig expressions

10.12

Use sine ratio to calculate angles and side (Sin = $\frac{o}{h}$ )

10.13

Use cosine ratio to calculate angles and side (Cos = $\frac{a}{h}$ )

10.14

Use tangent ratio to calculate angles and side (Tan = $\frac{o}{a}$ )

10.15

Combination of SohCahToa questions

10.16

Law of sines

10.17

Law of cosines

10.18

Sine graph: y = sin x

10.19

Cosine graph: y = cos x

10.20

Tangent graph: y = tan x

10.21

Cotangent graph: y = cot x

10.22

Secant graph: y = sec x

10.23

Cosecant graph: y = csc x

10.24

Graphing transformations of trigonometric functions

10.25

Determining trigonometric functions given their graphs

10.26

Quotient identities and reciprocal identities

10.27

Pythagorean identities

10.28

Sum and difference identities

10.29

Double-angle identities

10.30

Word problems relating ladder in trigonometry

10.31

Word problems relating guy wire in trigonometry

10.32

Other word problems relating angles in trigonometry

SOHCAHTOA is actually a memory aid to memorize how to calculate sine, cosine and tangent of an angle. SOH: sine = opposite over hypotenuse; CAH = adjacent over hypotenuse; and TOA = opposite over adjacent. Besides using them separately, the sine, cosine, and tangent ratios can be used together to solve trigonometry problems.

Basic Concepts: Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ ), Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ ), Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ ), ASTC rule in trigonometry (**A**ll **S**tudents **T**ake **C**alculus)

Related Concepts: Law of sines, Law of cosines, Find the exact value of trigonometric ratios, Trigonometric ratios of angles in radians

- 1.Find the length of $\overline{ BC}$

- 2.Find the length of $\overline{ BD}$

10.

Trigonometry

10.1

Converting between degrees and radians

10.2

Radian measure and arc length

10.3

Angle in standard position

10.4

Coterminal angles

10.5

Reference angle

10.6

Find the exact value of trigonometric ratios

10.7

ASTC rule in trigonometry (All Students Take Calculus)

10.8

Unit circle

10.9

Trigonometric ratios for angles in radians

10.10

Solving first degree trigonometric equations

10.11

Determining non-permissible values for trig expressions

10.12

Use sine ratio to calculate angles and side (Sin = $\frac{o}{h}$ )

10.13

Use cosine ratio to calculate angles and side (Cos = $\frac{a}{h}$ )

10.14

Use tangent ratio to calculate angles and side (Tan = $\frac{o}{a}$ )

10.15

Combination of SohCahToa questions

10.16

Law of sines

10.17

Law of cosines

10.18

Sine graph: y = sin x

10.19

Cosine graph: y = cos x

10.20

Tangent graph: y = tan x

10.21

Cotangent graph: y = cot x

10.22

Secant graph: y = sec x

10.23

Cosecant graph: y = csc x

10.24

Graphing transformations of trigonometric functions

10.25

Determining trigonometric functions given their graphs

10.26

Quotient identities and reciprocal identities

10.27

Pythagorean identities

10.28

Sum and difference identities

10.29

Double-angle identities

10.30

Word problems relating ladder in trigonometry

10.31

Word problems relating guy wire in trigonometry

10.32

Other word problems relating angles in trigonometry

10.1

Converting between degrees and radians

10.2

Radian measure and arc length

10.3

Angle in standard position

10.4

Coterminal angles

10.5

Reference angle

10.6

Find the exact value of trigonometric ratios

10.7

ASTC rule in trigonometry (All Students Take Calculus)

10.9

Trigonometric ratios for angles in radians

10.10

Solving first degree trigonometric equations

10.11

Determining non-permissible values for trig expressions

10.12

Use sine ratio to calculate angles and side (Sin = $\frac{o}{h}$ )

10.13

Use cosine ratio to calculate angles and side (Cos = $\frac{a}{h}$ )

10.14

Use tangent ratio to calculate angles and side (Tan = $\frac{o}{a}$ )

10.15

Combination of SohCahToa questions

10.24

Graphing transformations of trigonometric functions

10.25

Determining trigonometric functions given their graphs

10.26

Quotient identities and reciprocal identities

10.27

Pythagorean identities

10.28

Sum and difference identities

10.29

Double-angle identities

10.30

Word problems relating ladder in trigonometry

10.31

Word problems relating guy wire in trigonometry

10.32

Other word problems relating angles in trigonometry