Ch.10 Trigonometric identities & equations

Question 1

how would you prove the exact trig values for 30° and 60° ?

Answer 1

consider an equilateral triangle of ABC with the side being 2 units

then split it in half and find the missing side

lastly use SOH CAH TOA

Question 2

how would you prove the exact trig values for 45° ?

Answer 2

consider an isosceles right angled triangle PQR with 2 sides being 1

therfore the hypotenuse is square root of 2

lastly solve for SOH CAH TOA

Question 3

what are the 2 trig identities?

Answer 3

tanθ ≡ sinθ ÷ cosθ

and

sin²θ + cos²θ ≡ 1

Question 4

how would you prove the 2 trig identities?

Answer 4

consider a right angled triangle with hypotenuse of 1 and sides of y and x

solve for SOH CAH TOA for the first identity

use pythag for the second identity