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

User Wennie
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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}

Suppose cos(theta) = 2/7 was in quadrant 4. Use a trig identity to find the value-example-1
User Mxro
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