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6 problems match “inverse trigonometric functions”. Clear

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1. Arcsine of sine of 10 ●●○○○ 20 ptsEvaluate $\sin^{-1}(\sin 10)$, where $10$ is in radians. Round your answer to two decimal places.
2. Angle between y = x² and y = 1/x ●●○○○ 20 ptsFind the acute angle of intersection, in degrees, between the curves $y = x^2$ and $y = \dfrac{1}{x}$, measured between their tangents at the point of intersection. Round to two decimal places.
3. Cosine of arcsecant plus arccosecant ●●○○○ 20 ptsEvaluate $\cos\left(\sec^{-1}x+\csc^{-1}x\right)$ for $|x|\geq 1$. (The answer is a single number, the same for every such $x$.)
4. 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.
5. 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.
6. 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.