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Evaluating Trigonometric Expressions and Equations of Lines

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12. Use a half-angle identity to find the exact value of cos 105 degrees.

13. Solve tan(x) - sqrt(8) = 0 for 0 <= x <= 2*pi.

14. Solve 4sin^2(x) - 1 = 0 for principal values of x. Express the solution(s) in degrees.

15. Solve cos^4(x) - 1 = 0 for all real values of x.

16. Write the equation 2x + 5y - 3 = 0.

17. Write the standard form of the equation of a line for which the length of the normal is 7 and the normal makes an angle of 150 degrees with the positive x-axis.

18. Find the distance between P(-1, 4) and the line with equation 4x - 2y + 3 = 0.

19. Find the distance between the lines with equations x - 2y - 3 and y = 1/2x - 2.

20. Find an equation of the line that bisects the acute angles formed by the lines with equations 3x + y + 6 = 0 and 2x - y - 1 = 0.

Bonus:

Express the sqrt(tan^2(theta)/sec^2(theta) + cot^2(theta)*sec^2(theta) in terms of sin(theta).

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Solution Summary

This solution evaluates the trigonometric equations and lines in an attached Word document.

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