MCR3U0 Name ______
Trigonometric Equations
· Trigonometric equations can be solved by using
- pencil and paper methods similar to those used to solve algebraic equations, to
give exact answers
- a graphing calculator or graphing software, to give approximate answers.
10/11/2014
MCR3U0 Name ______
1. Solve each equation for .
a) b)
c) d)
e) f)
g) h)
2. Solve each equation for .
a)
b)
c)
d)
e)
f)
3. Solve each equation for . Express answers as exact values or as approximate values, to the nearest hundredth of a radian.
a)
b)
c)
d)
4. Solve each equation for . Express answers as exact values or as approximate values, to the nearest tenth of a degree.
a)
b)
c)
d)
5. Measurement A rectangle has one vertex at the origin and sides along the coordinate axes. The area of the rectangle is given by the function
A(q) = ½cos q sin q½.
a) What are the coordinates of the vertices of the rectangle?
b) Can the area equal 0.25 square units? If so, what is the value(s) of q that produces this area?
c) What is the minimum area of the rectangle? For what values of q does this occur?
d) What is the maximum area?
6. Daylight In a given region, the number of daylight hours varies, depending on the time of year. This variation can be modelled by the function
d(t) = 5 sin , where d(t) is the number of hours of daylight, and t represents the number of days after January 1. Find two days when the approximate number of daylight hours is 16.
7. Medicine The temperature of a patient during a 9-day illness is given by
T(t) = 39.1 + 2.1 sin , where t is the number of days from the start of the illness, and T (t)is the patient’s temperature, in degrees Celsius.
a) Does the patient’s temperature reach 41°C? If so, on what day?
b) What is the patient’s temperature at the end of the illness?
SOLUTIONS
1a) b) c) d)
e) f) g) h)
2 a) b) c)
d) e) f)
3 a) b) c)
d)
4 a) b) c)
d)
10/11/2014