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TRIGONOMETRY III | FORM 4 LEVEL | PAPER 2 QUESTIONS | SECTION B(a) Complete the table for y = Sin x + 2cos x. (2mks)
(b) Draw the graph of y= sin x + 2 Cos x using a scale of 1cm to represent 30o on x-axis and 2cm to represent 1 unit on y-axis. (3mks)
(c) Solve sin x + 2 cos x = 0 using the graph. (2mks)
(d) Find the range of values of x for which y≤-0.5. (3mks)
Form 4 Mathematics
Determine the amplitude and the period of the function y = 3 sin(2x + 40°).
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Form 4 Mathematics
The table below shows some values of the curves y = 2 cos x and y = 3 sin x.
(a) Complete the table for values of y = 2 cos x and y = 3 sin x, correct to 1 decimal place. 
On the grid provided, draw the graphs of y = 2 cos x and y = 3 sin x for 0° ≤ x ≤ 360°, on the same axes.
(c) Use the graph to find the values of x when 2 cos x — 3 sin x = 0 (d) Use the graph to find the values of y when 2 cos x = 3 sin x.
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Form 4 Mathematics
State the amplitude and the phase angle of the curve y = 2 sin ( 3/2 x — 30°)
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Form 4 Mathematics
Determine the amplitude, period and the phase angle of the curve: y = 5/2 sin (4θ + 60°)
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Form 3 Mathematics
Find in radians, the values of x in the interval 0c ≤ x ≤ 2πc for which 2 cos2x - sin x = 1. (Leave the answer in terms of π)
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Form 3 Mathematics
Given that x is an acute angle and cos x = 2/5 √5 find, without using mathematical tables or a calculator, tan (90-x).
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Form 4 Mathematics
The equation of a curve is given by y= 1 + 3sin x.
(a) Complete the table below for y = 1 + 3 sin x correct to 1 decimal place 
(b) (i) On the grid provided, draw the graph of y - 1 + 3 sin x for 0° ≤ x ≤ 360°.
ii) State the amplitude of the curve y = 1 + 3 sin x. c) On the same grid draw the graph of y = tan x for 90° ≤ x ≤ 270°. d) Use the graphs to solve the equation ; 1+3 sin x = tan x for 90° ≤ x ≤ 270°.
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Form 4 Mathematics
Determine the amplitude and period of the function, y = 2 cos (3x — 45)°.
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Form 4 Mathematics
a) Complete the table below, giving your values correct to 2 decimal places.
Answer
Form 4 Mathematics
(a) Complete the table below, giving the values correct to 1 decimal place.
b) On the grid provided, using the same scale and axes, draw the graphs of y = 2 sin (χ+20)0 and y = √3 cos χ for 00 ≤ χ ≤ 2400.
c) Use the graphs drawn in (b) above to determine: i) the value of χ for which 2sin (χ + 20) = √3 cos χ; ii)the difference in the amplitudes of y =2sin(χ + 20) and y =√3 cos χ.
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Form 4 Mathematics
a) Complete the table below, giving your values correct to 2 decimal place.
b) Using the grid provided and the table in part (a) draw the graphs of Y = tan Ө and y = sin 2Ө.
c) Using your graphs, determine the range of values for which tan Ө>Sin 2Ө for 00 ≤ Ө ≤ 900.
Answers
Form 4 Mathematics
The table below shows values of x and y for the function y = 2 sin 3x° in the range 00 ≤ x ≤ 1500
(a) On the grid provided, draw the graph of y = 2 sin 3x.
(b) From the graph determine the period.
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Form 4 Mathematics
(a) Complete the table below, giving the values correct to 2 decimal places.
(b) On the grid provided and using the same axes draw the graphs of y = cos x° and y= sin x°— cos x° for 0° ≤ x ≤ 180°.Use the scale; 1 cm for 20°on the x-axis and 4cm fort unit on the y-axis.
(c) Using the graph in part (b): (i) solve the equation sin x° — cos x° 1.2; (ii) solve the equation cos x°= 1/2 sinx; (iii) determine the value of cos x° in part (c) (ii) above.
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Form 4 Mathematics
a) complete the table below, giving the values correct to 2 decimal places.
b) On the grid provided, draw the graphs of y=sin 2x and y=3cosx-2 for 00 ≤ x ≤3600 on the same axes.
Use a scale of 1 cm to represent 300 on the x-axis and 2cm to represent 1 unit on the y-axis. c) Use the graph in (b) above to solve the equation 3 Cos x – sin 2x = 2. d) State the amplitude of y=3cosx-2.
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Form 4 Mathematics
Find in radians, the values of x in the interval 00≤ x ≤ 2π0+ for which 2 cos 2x=1.
(Leave the answers in terms of π )
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Form 4 MathematicsSolve the equation 4 sin2 Ө+4 cos Ө =5 For 0o ≤ Ө ≥ 360o give the answer in degrees
aNSWER
Form 4 Mathematics
a) Complete the table given below in the blank spaces.
Give your answer to the nearest degree.
Answer
Form 4 MathematicsGiven that sin ( x + 30)0 = cos 2x0 for 00, 00 ≤ x ≤900 find the value of x. Hence find the value of cos23x0.
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