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18 problems match “trigonometric functions”. Clear

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.
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.
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 $y$ .
Max-min difference of a shifted sine ●●○○○ 20 ptsFind the difference between the maximum and minimum values of the function $y=2\sin\left(\frac{\pi x}{6}-\frac{\pi}{3}\right)$ for $0\leqslant x\leqslant 9$ . Round to two decimal places.
Direction of a vector in quadrant II ●●○○○ 20 ptsFind the direction of the vector $(-4,3)$ , measured as the counterclockwise angle from the positive $x$ -axis in degrees. Round to two decimal places.
Complex line integral of 1/(1+z^2) ●●●○○ 50 ptsEvaluate $\int_1^{1+i}\frac{1}{1+z^2}\,dz$ along the straight line segment from $z=1$ to $z=1+i$ . Give the real part and the imaginary part of the result separately. Round each to two decimal places.
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.
Rotating a line to equal intercepts ●●●○○ 50 ptsThe line $y=10-2x$ is rotated anticlockwise about the origin through an angle $\theta$ , where $0 \le \theta \le 90$ (in degrees). The image has $x$ -intercept $(p,0)$ and $y$ -intercept $(0,q)$ . Determine $\theta$ such that $p=q$ . Round to two decimal places.