Question

Suppose cos(theta) = 2/7 was in quadrant 4. Use a trig identity to find the value of sin(theta).

Answer 1

In quadrant 4, we need to graph a reference right triangle:

Where cosθ= adjacent side/ hypotenuse . Therefore, 2 is the value for the adjacent side and the hypotenuse is equal to 7.

Now, to find the opposite side, we need to use the Pythagorean theorem:

`c^2=a^2+b^2`

Where c represents the hypotheses,

a represents the adjacent side and b represents the opposite side.

Solve the equation for b, then:

`b=\sqrt[]{c^2-a^2}`

Replacing the values:

`b=\sqrt[]{(7)^2-(2)^2}`

Hence:

`b=3\sqrt[]{5}`

Finally, we have that sin(theta)= opposite side / hypotenuse.

Replacing with the values, therefore:

`\sin \theta=\frac{3\sqrt[]{5}}{7}`