Question

If sinθ = 3/4 and is in the first quadrant, then cosθ = _____.

Answer 1

The trick here is to recognize that "sin omega = 3/4" provides us with the length of the opposite side of a first-quadrant triangle and the length of the hypotenuse; they are 3 and 4 respectively.

Find the length of the adjacent side (x) using the Pythagorean Theorem: 3^2 + x^2 = 4^2, or x^2 = 16 - 9 = 7. Then the length of the adj. side, x, is sqrt(7).

The cosine of omega is adj / hyp, or sqrt(7) / 4.

Answer 2

Answer: The answer is
`\cos \theta=(√(7))/(4).`

Step-by-step explanation: Given that

`\sin \theta=(3)/(4)` and
`\theta` is in Quadrant I.

We are to find the value of
`\cos \theta.`

We have the following trigonometric identity :

`\sin^2\theta+\cos^2\theta=1\\\\\Rightarrow \cos^2\theta=1-\sin^2\theta\\\\\Rightarrow \cos \theta=\pm√(1-\sin^2\theta)\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\left((3)/(4)\right)^2}\\\\\\\Rightarrow \cos \theta=\pm\sqrt{1-(9)/(16)}\\\\\\\Rightarrow \cos \theta=\pm\sqrt{(7)/(16)}\\\\\\\Rightarrow \cos \theta=\pm(√(7))/(4).`

Since
`\theta` lies in the first quadrant, so cosine of
`\theta` will be positive.

Thus,

`\cos \theta=(√(7))/(4).`