Trigonometric Ratios

Solve Basic Trigonometric Functions

Learning Outcome:

Solve the equations such as

 $\sin\ \theta=k$  ,  $\cos\theta=k$  and  $\tan\theta=k$  .

Remember to think about which quadrant will give you positive or negative trigonometric ratios.

You need to give your answer(s) according to the ranges given.

If $0\degree\le\theta\le180\degree$  , then your answers only will be in quadrant 1 and 2.

Multiple Select

Find the value of

$$\theta$$ for  $$\sin\theta=\frac{1}{\sqrt{2}}$$  , where  $$0\degree<\theta<360\degree$$  .  Choose ALL correct answers. 

• 45

• 225

• 315

• 135

Please use appropriate unit for your angle.

Check your calculator mode.

Do you remember what is

 $\operatorname{cosec}\ \theta,\ \sec\theta$  and  $\cot\theta\ ?$  

Multiple Select

Solve   $$\sec\theta=\sqrt{2},\ \ 0<\theta<3\pi$$ . 

Choose ALL correct answers. 

• $$\frac{\pi}{12}$$  

• $$\frac{9\pi}{4}$$  

• $$\frac{\pi}{4}$$  

• $$\frac{5\pi}{4}$$  

• $$\frac{7\pi}{4}$$  

If you have the range in terms of $\theta$ ,

then, the angle involve in the question is  $2\theta$  , you need to multiple the range by 2. 

e.g.  $0<\theta<2\pi\ \ \ \ \ \Longrightarrow\ \ \ 0<2\theta<4\pi$  

Fill in the Blanks

Solve $\tan\ 2x=-\sqrt{3}$  , where  $0\degree<x<360\degree$  .

(Tips* : type all your answers in ascending orders without the simbol  $\degree$  and without space).

Multiple Choice

Solve $$\sin\left(\alpha+10\degree\right)=0.32\$$  to two decimal places, where  $$0\degree<\alpha<360\degree$$  .

• $$18.66\degree,\ 161.34\degree$$  

• $$8.66\degree,\ 151.34\degree$$  

• $$18.66\degree,\ 341.34\degree$$  

• $$8.66\degree,\ 331.34\degree$$  

What is the relation between $\sin x$  and  $\cos x$  ?

(Hint: refer Learning Outcome 7.1(b) )

Multiple Choice

Solve

$$\sin A=\cos A,$$  where  $$0<A<2\pi$$  

• $$A=\frac{\pi}{4},\frac{5\pi}{4}$$  

• $$A=\frac{\pi}{4},\frac{3\pi}{4}$$  

• $$A=0,\ \pi,\ 2\pi$$  

• $$A=\frac{\pi}{4},\ \ \frac{7\pi}{4}$$  

Fill in the Blanks

Solve $\left(\cos x\right)^2=\frac{1}{4}$  , where  $0\degree\le x\le360\degree$  

 (Tips* : type all your answers in ascending orders without the simbol  degree ° and without space).

You can re-attempt to get the correct answers!