Trigonometry Answers

sin(theta+pi/6)+cos(theta+pi/3)=cos theta

A 6.7m totem pole is being erected on Vancouver Island.  The carvers know that the tethers holding the pole in place need to meet the ground at an angle of 39° for maximum stability.  Albert states that they should use the cosine ratio to determine how the long the tethers should be. Stanley argues that they should use the sine ratio.

Find the value of the x. Y is 30 degrees and side is 14

The L and C State Building is 1, 250 m tall. What is the angle of elevation of 

the top from a point on the ground 1,760 m from the base of the building?

Nick runs around the perimeter of a circular track at 11 ft/sec. The track has a radius of 99 yd. After 30 seconds, Nick turns and runs to the center of the track along a straight (radial) line. Upon reaching the center, he turns and runs away along a different radial line to his starting position on the perimeter.

How far has Nick traveled once he has returned to his starting position?

distance =  feet

Ali is building a theater in the man-cave in his new house. He cannot recall the exact dimensions, but he knows that the length is 4 feet longer than the width, and the area is 525 square feet. Help Ali and the contractor solve for the length and width of his theater. Show all of your work and explain your answer.

Bold

Italic

Underline

Determine the value of sin2x given that tan^2x=81/49 and Pi<x<3pi/2

 The population of mice in Canterbury High School fluctuates from a minimum of 80 mice to a maximum of 420 mice. This population can be modelled as a function of time in months from Jan. 1st, by a cosine function. At the beginning of the year (January 1st), the population is at its least (80 mice) . After 3 months the population reaches its maximum (April 1st). On Canada Day (July 1st) the population goes back down to its minimum of 80. Three months later it reaches the maximum again (Oct. 1st). (And so on.)

(a) Draw a detailed graph of this situation for 1 year.

(b) Determine the equation of this function as a cosine function and a sine function that

describes the population of the mice in CAnterbury High School.

(c) Determine the time in months (to 1 decimal place) for one year, when the population is

above 165 mice.