Question

(sin ∅)² is usually written sin²∅. however, the first must be in your calculator. Also, sin ∅² means first do ∅², then take the sine. If sin ∅=0.6 and π/2 ≤ ∅ ≤ π, find the following or say "impossible with no calculator."a) (sin∅)²b) sin² ∅c) sin ∅²d) cos ∅e)3 cos² ∅f)(3 cos ∅)²

Answer 1

a) 0.36 Just notation, that is the square of sin(angle)

b) 0.36 Just notation, that is the square of sin(angle)

c) Impossible with no calculator

d) sqrt(1-0.36) = 0.8 (Trigonometric identity )

e) 3*(0.8)^2 = 1.92 Just doing arithmetic operations

f) (3*0.8)^2 = 5.76 Just doing arithmetic operations

cos(3 pi/4) = -sqrt(2)/2

sin(11*pi/6) = -1/2

sin(-2*pi/3) = -sqrt(3)/2

tan(5pi/4) = 1

All of those results are based on trigonometric identities

cos(angle) = sqrt(1 - (5/13)^2) = 0.92

tan(angle) = (5/13)/0.92=0.41