Questions: In 5-10, match each expression with the correct value. Drag each of the values given above into the appropriate area to match the expressions below. 5. cos(75°) 8. tan(-π/8) 6. tan(π/12) 9. tan(67.5°) 7. sin(3π/8) 10. cos(67.5°)

Solution Steps

To solve these trigonometric expressions, we will use Python's math library, which provides functions to calculate sine, cosine, and tangent values. We will convert degrees to radians where necessary since Python's trigonometric functions use radians.

Using the cosine function, we find: \[ \cos(75^\circ) \approx 0.2588 \]

Using the tangent function, we find: \[ \tan\left(-\frac{\pi}{8}\right) \approx -0.4142 \]

Using the tangent function, we find: \[ \tan\left(\frac{\pi}{12}\right) \approx 0.2679 \]

Using the sine function, we find: \[ \sin\left(\frac{3\pi}{8}\right) \approx 0.9239 \]

Using the tangent function, we find: \[ \tan(67.5^\circ) \approx 2.4142 \]

Using the cosine function, we find: \[ 10 \cdot \cos(67.5^\circ) \approx 3.8268 \]

Final Answer