Question

If sin θ = 3 over 7 and tan θ < 0, what is the value of cos θ?

Answer 1

Hello Dear.

Given ⇒

Sin Ф = 3/7

∵ Sin Ф = P/H
∴ Let the Perpendicular and the Hypotenuse of the Right angled triangles be 3x and 7x respectively.

Now,
Using Pythagoras Theorem,

H² = P² + B²
⇒ B² = H² - P²
⇒ B² = (7x)² - (3x)²
⇒ B² = 49x² - 9x²
⇒ B² = 40x²
⇒ B = 2x√10 

Now,

∵ Cos Ф = B/H
∴ Cos Ф = (2x√10)/7x
⇒ Cos Ф = 2√10/7


Hence, the Value of the Cos Ф is 2√10/7.


Hope it helps.