Trig Equations

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March 2013

8.1   Simplify as far as possible:

8.1


OR




8.2   Simplify WITHOUT the use of a calculator:

8.2


OR




8.3   Prove that

8.3



8.4   Prove that for any angle θ :

8.4



8.5   If x = cos200, use QUESTION 8.4 to show that

8.5


March 2012

11.1 If

determine the following in terms of p:

11.1.1   sin 241°

11.1.1





11.1.2   cos 61°

11.1.2



11.1.3   cos 122°

11.1.3



11.1.4   cos73° cos15° + sin73° sin15°

11.1.4



11.2
11.2.1 Prove the identity:


11.2.1



11.2.2 Determine a value of x in the interval [0° ; 180°] for which the identity is not valid.

11.2.2



11.3
11.3.1 Given: sin x = cos2x -1. Show that

11.3.1



11.3.2 Determine the general solution of the equation:
sin x = cos 2x - 1.

11.3.2


OR




11.4 Determine the value of:
tan1°×tan2°×tan3°×tan4°×... ×tan87°×tan88°×tan89°.

11.4


OR




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