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Overview
Accuplacer Advanced Algebra and Functions
Trigonometry
26. Right triangle trigonometry
26.5 Trigonometric ratios SOH CAH TOA in each quadrant and special triangles
SOH CAH TOA in Each Quadrant and Special Triangles
Learn the SOH CAH TOA formula, discover how sine, cosine and tangent change sign in each quadrant, and apply 30-60-90 and 45-45-90 triangles.
What You'll Learn
SOH CAH TOA gives sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent
In quadrant I every ratio is positive, in quadrant II only sine is positive, in quadrant III only tangent is positive, and in quadrant IV only cosine is positive
The 45-45-90 triangle has sides in the ratio 1 to 1 to square root of 2, and the 30-60-90 triangle has sides in the ratio 1 to square root of 3 to 2
A reference angle lets you reuse a special triangle's ratios for any angle, only the sign changes depending on the quadrant
These exact values come up constantly in later trigonometry and calculus, so it pays to memorize them well
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Learning resources
TEST-PREP Curriculum Aligned