Please answer all the following questions With full detail and explanation On paper please!Thanks very much

7. Given cot' 0-- =0, -5 50s a. Algebraically solve for 0. State the solution(s) as exact radian values. (2 marks) b. Use technology to graphically determine the quadrant IV solution. Explain your steps. State the solution as a decimal approximation rounded to the nearest thousandth. (1 mark) Without using your calculator, show a numerical verification using exact radian values using the quadrant Ill solution, Show at least 4 steps in your verification. (1 mark 8. Given sin 0 cos0 1+cos0 1-cos 0 tan 0 a. Prove the identity. (2 marks) Determine one general solution (in radians) for all non-permissible values. (1 mark) 9. Use the Sum and Difference Identities from the Math 30-1 Formula Sheet to answer the following two questions. Determine the exact value of tan . State the answer in simplest form. (Hint: The solution will be a binomial.) (2 marks) b. Simplify sin 2 -0 -cos | 0+2 (2 marks) 6. Given a sinusoidal function with a maximum at (180,2) and a consecutive minimum at (90%,-3). a. Sketch the curve showing at least two cycles. Label the amplitude & period on your graph (2 marks) 270 Complete the following chart for the sinusoidal curve. (2 marks) Amplitude Period Equation of the Sinusoidal Axis (midline) The total number of zeros in the Interval [-200%,100] 10. Algebraically solve the following equations: a. Algebraically solve cos 20-1-2sin0,-180' se