Calculate angle using arccos, arcsin, arctan
CONCEPTS
BEGINNER 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
• Angle of inclination / ascent / elevation all mean the same thing. It is the angle between horizontal line & the slanted line or hypotenuse (angle C in the triangle above)
ADVANCED 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
BEGINNER QUESTIONS
Question 1 Write expression to solve for θ (see picture below)?
-- Answer -- θ = sin⁻¹ (4/7)
Question 2 Write an expression to find the angle of elevation between the staircase & floor (see picture below)?
-- Answer -- sin⁻¹ (10 / 26)
Angle of elevation is between the horizontal and angled line, sin⁻¹ (opp / hyp) = sin⁻¹ (10/26)
ADVANCED QUESTIONS
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