Question

The terminal side of an angle θ in standard position is in quadrant 1. If sinθ=0.8, find cosθ.

Answer 1

Answer:

$cos\theta=\frac{3}{5}$

Step-by-step explanation:

Since $sin\theta=0.8$ is the same as $sin\theta=\frac{4}{5}$ and $sin\theta=\frac{opposite}{hypotenuse}$, then we know that the side opposite to the angle $\theta$ is 4 units and the hypotenuse is 5 units.

Because $cos\theta=\frac{adjacent}{hypotenuse}$, then we have to find the adjacent side to the angle $\theta$ using the Pythagorean Theorem:

$a^2+b^2=c^2\\\\(adjacent)^2+(opposite)^2=(hypotenuse)^2\\\\(adjacent)^2+4^2=5^2\\\\(adjacent)^2+16=25\\\\(adjacent)^2=9\\\\adjacent=3$

Therefore, since the adjacent side is 3 units, then $cos\theta=\frac{3}{5}$