Still Confused?

Try reviewing these fundamentals first

Algebra

Combining transformations of functionsTrigonometry

Sine graph: y = sin xTrigonometry

Tangent graph: y = tan xTrigonometry

Secant graph: y = sec x- Home
- Precalculus
- Trigonometry

Still Confused?

Try reviewing these fundamentals first

Algebra

Combining transformations of functionsTrigonometry

Sine graph: y = sin xTrigonometry

Tangent graph: y = tan xTrigonometry

Secant graph: y = sec xStill Confused?

Try reviewing these fundamentals first

Algebra

Combining transformations of functionsTrigonometry

Sine graph: y = sin xTrigonometry

Tangent graph: y = tan xTrigonometry

Secant graph: y = sec xNope, got it.

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Get Started Now- Lesson: 1a27:03
- Lesson: 1b34:05
- Lesson: 1c19:26
- Lesson: 221:41

After learning all the graphs of basic trigonometric functions, in this lesson, we are going to go a little bit further on how the graphs will be transformed as the functions change. The general form for the equation of trig functions is y = *f* [B(x + c)] + D, where *f* refers the trig function; A refers to the amplitude/steepness; B represents the period of the graph; C refers to phase shift (left or right) and D represents vertical shift (up or down). We will learn how to graph the trig function for multiple periods; state the vertical displacement, phase shift, period and amplitude; and also find the domain and range of the transformed functions.

Basic Concepts: Combining transformations of functions, Sine graph: y = sin x, Tangent graph: y = tan x, Secant graph: y = sec x

Related Concepts: Ferris wheel trig problems, Tides and water depth trig problems, Spring (simple harmonic motion) trig problems

- 1.For each trigonometric function:

(i) Graph the trigonometric function for one period.

(ii) State the vertical displacement, phase shift, period, and amplitude.

(iii) State the domain and the range.a)$y = 2\sin \frac{\pi }{4}(x + 3) + 1$b)$y = 3\sec (\frac{\pi }{2}x - \pi ) - 1$c)$y = - 2\sin (4x + 4\pi ) - 3$ - 2.For the trigonometric function: $y = - \tan \left( {\;\frac{x}{3} - \frac{\pi }{6}\;} \right)$

i) Graph the trigonometric function for two periods.

ii) State the domain and the range.

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

We have over 830 practice questions in Precalculus for you to master.

Get Started Now10.1

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