A104 TrigonometryWB 10

sin (θ )

cos (θ )

tan (θ )

Describe the features of each graph

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A104 Trigonometry

WB 11

Symmetry of sine graph

Symmetry of cosine graph

Symmetry of tangent graph

Also For any angle ϴ, check these on your calculator

sin (−θ )=−sin (θ ) sin(- 25) =

cos (−θ )=cos (θ ) cos(-240) =

tan (−θ )=−tan (θ ) tan(- 110) =

Sine is an ‘even’ graph. Cosine and Tangent are odd graphs

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A104 TrigonometryWE12 Trig exact values :

Use the diagrams to find exact values of sin / cos / tan for angles 30, 45 and 60

complete the table

0 ° 30 ° 45 ° 60 ° 90 °

sin x

cos x

tan x

3

60˚ 60˚

60˚

2

2 2

45˚

1

1

√2

A104 TrigonometryWB13 Show that

a) cos230+sin 230=1

b) sin 330=−12

tan60+ 1tan 60

= 1sin 60 cos60

WB14Given that tanθ=3

4a) Find sin θ and cosθb) solve the simultaneous equations 5 x sin θ−11= y and 3 x+5 y cosθ=1

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A104 Trigonometry

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A104 TrigonometryWB15

The graph shows the Function: f(x) = Sinθ + ka) Write down the value of kb) What is the smallest positive value of θ that gives a minimum point?c) What is the value of Sinθ at this point?

WB16

The graph shows the Function: f(x) = Cos(θ + k)

a) Write down the value of kb) What is the value of θ at x?c) What are the coordinates of the minimum?d) What is the value of Cosθ at y intercept?

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