Trigonometry Quiz
Instructions
Please answer the following questions to the best of your ability. Each question is open-ended, and you should provide your answer in the space provided.
- Define the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) in terms of a right triangle.
- Given a right triangle where one angle measures 30 degrees and the length of the opposite side is 5 units, calculate the length of the hypotenuse.
- Explain how to derive the Pythagorean identity, ( \sin^2(\theta) + \cos^2(\theta) = 1 ), using the unit circle concept.
- If the angle ( \theta ) is in standard position and has coordinates ( (3, 4) ) on the terminal side, find ( \sin(\theta) ) and ( \cos(\theta) ).
- Using the law of sines, solve for angle ( C ) in triangle ABC given that side ( a = 10 ) units, side ( b = 8 ) units, and angle ( A = 30^\circ ). Provide your answer rounded to two decimal places.
Good luck!