Pre-Calculus Trig 5.3

Find the exact value of Trigonometric expressions: (sin45°)( tan45°) (secπ/4)(cotπ/4)

(sin45°)( tan45°) = √2/2(1) = √2/2 √2(1) = √2

Find the exact value of Trigonometric expressions: π/6 = 30° π/3 = 60°

First, form a right triangle with π/6 = 30° and π/3 = 60°. set the hypotenuse = 2 and treat the triangle like it is equilateral. This will make it so each leg is equal to 2. leg a on the original triangle is half of the equilateral's leg, which is 1. since c = 2 and a = 1 then 1^2 + b^2 = c^2 which works out to b=√3. Using π/6 = 30° and π/3 = 60° and complementary angles, we can work the rest of the functions out using or formulas.

Exact value of trig function π/4 = 45°

if θ = 45° then the corresponding angle is also 45°. if sides are unknown we can substitute 1 for the length of the legs and use the pythagorean theorem. (1^2 + 1^2 = c^2) = (2 = c^2) = (c = √2) Thus: sinπ/4 = sin45° = b/c = 1/√2 = √2/2 cosπ/4 = cos45° = a/c = 1/√2 = √2/2 tanπ/4 = tan45° = sin45°/cos45° = 2/√2/2 = 1 cotπ/4 = cot45° = 1/tan45° = 1/1 = 1 secπ/4 = sec 45° = 1/cos45° = 1/1/√2 = √2 cscπ/4 = csc 45° = 1/sin45° = 1/1/√2 = √2