FROM THE GIVEN VALUES OF TWO TRIG FUNCTIONS FIND THE VALUE

Problem 1 :

Given that sin A = 4/5, 0 < A < 90° and that cos B = 2/3, 0 < B < 90°, find without using a calculator the value of

a) tan A     b) sin B     c) cos (A + B)     d) sin (A + B)

Solution:

We have,

sin A = 4/5 and cos B = 2/3

a) tan A = sin A / cos A

sin A = 4/5 and cos A = 3/5

tan A = (4/5)/(3/5)

tan A = 4/3

b)

c)

cos(A + B) = cosA cosB - sinA sinB

d)

sin(A + B) = sinA cosB + sinB cosA

Problem 2 :

Given that cosec C = 5/3, 0 < C < 90° and that sin D = 5/13, 90° < D < 180°, find without using a calculator the value of

a) cos C     b) cos D     c) sin (C - D)     

Solution:

We have,

cosec C = 5/3 and sin D = 5/13

a)

b)

c)

sin(C - D) = sinC cosD - cosC sinD

Problem 3 :

a.   Given that cos A = 7/9, 0 < A < 90°, find the exact value of sin A/2 without using a calculator.

Solution:

b. Given that cos B = -3/8, 90° < B < 180°, find the value of cos B/2, giving your answer in the form k√5.

Solution: