Construct a right triangle satisfying the following and use the sides of this triangle to determine the formulas of all the remaining trigonometric functions. Assume in each case that 0 < 𝜃 < 𝜋/2.

Question

(a) sin 𝜃 = 2/3

cos=

tan=

cot=

sec=

csc=

Answer 1

hypotenuse =3, opposite side = 2, adjacent side = sqr(9-4) = sqr5 = about 2.2, in Quadrant I

cos(theta) = sqr5/3 = about 2.2/5

tan(theta) = 2/sqr5 = about 2/2.2 = 1/1.1

cot(theta) = 1/tan(theta) = sqr5/2 = about 1.1

sec(theta) = 1/cos(theta) = 3/sqr5 = about 5/2.2

csc(theta) = 1/sin(theta) = 3/2 = 1/5