Calculate angle using arccos, arcsin, arctan

CONCEPTS

Angles in Right Triangles

• cos⁻¹ (b/c) = arcsin (b/c) = θ

• sin⁻¹ (a/c) = arcsin (a/c) = θ

• tan⁻¹ (b/a) = arctan (b/a) = θ

Tip

• Create right triangles from a figure and find the side lengths. Then use sohcahtoa to find the angles.

PRACTICE PROBLEMS

Question 1 What is the cos of the smallest angle in right triangle ACD (see figure below)

-- Answer -- 7 / √58

The smallest angle is opposite the smallest side, which is AC or angle D. Cos D = 7 / √58

ACT PRACTICE PROBLEMS

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