Given that sin theta cos theta =7/50 and 0^0 < theta < 90^0. Find the value of cos theta.?

Help pls...

2 Answers
Jun 22, 2018

7/(5*sqrt(2)),1/(5*sqrt(2))

Explanation:

Solving the equation
sin(theta)*cos(theta)=7/50
in the given interval we get

x_1=-2arctan(7-5sqrt(2))

x_2=2arctan(1/7(5sqrt(2)-1))
so we gat

cos(x_1)=7/(5sqrt(2))

cos(x_2)=1/(5sqrt(2))

Jun 22, 2018

8^@13, 81^@87

Explanation:

sin t.cos t = 7/50
Use trig identity: sin 2t = 2sin t.cos t
In this case:
sin t.cos t = (sin 2t)/2 = 7/50
sin 2t = 15/50 = 7/25
Calculator and unit circle give 2 solutions for 2t:
2t = 16^@26, and 2t = 180 - 16.26 = 163^@74
a. 2t = 16.26 + k360
t = 8^@13 + k180^@
b. 2t = 163.74 + k360
t = 81^@87 + k180^@
Answers for (0, 90)
8^@13, 81^@87
cos (8.13) = 0.99
cos (81.87) = 0.14