Trigonometry › Angles and radians

Point on the terminal side

Solve the first problem 15 problems

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1. Sine and cosine from terminal side ●○○○○ 10 ptsThe terminal side of angle $\alpha$ lies on the ray $y = -\frac{3}{4}x$ with $x > 0$. Find the value of $2\sin\alpha + \cos\alpha$. Give your answer as a decimal.
2. Sine minus cosine from a terminal point ●○○○○ 10 ptsThe terminal side of angle $\alpha$ passes through the point $P(-2,4)$. Find the value of $\sin\alpha - \cos\alpha$. Round to two decimal places.
3. Abscissa from tangent of terminal side ●○○○○ 10 ptsThe terminal side of angle $\alpha$ passes through the point $P(x, -6)$, and $\tan\alpha = -\frac{3}{5}$. Find the value of $x$.
4. Cosine shifted by 3π/2 from a terminal side ●●○○○ 20 ptsGiven that the terminal side of angle $\theta$ passes through $(-2, 3)$, find the value of $\cos\left(\theta + \frac{3\pi}{2}\right)$. Round to two decimal places.
5. Sine plus cosine on a ray ●●○○○ 20 ptsGiven that the terminal side of angle $\theta$ lies on the ray $y=2x$ with $x\le 0$, find the value of $\sin\theta+\cos\theta$. Round to two decimal places.
6. Coordinate on the terminal side ●●○○○ 20 ptsGiven that point $P(-2, y)$ lies on the terminal side of angle $\theta$, and $\sin\theta = \frac{\sqrt{5}}{5}$, find $y$.
7. Trig expression from a point on the terminal side ●●●○○ 50 ptsLet $\alpha$ be an angle in the second quadrant. The point $P(x, \sqrt{5})$ lies on the terminal side of $\alpha$, and $\cos\alpha = \frac{\sqrt{2}}{4}x$. Find $4\cos\left(\alpha + \frac{\pi}{2}\right) - 3\tan\alpha$. Round to two decimal places.

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