Sine and Cosine Examples & Practice Questions

Here are some Sine and Cosine worked examples. There will then be some questions for you to practice.

Enjoy!

There are FOUR question types where the sine and cosine rules would be applied. Learn these rules and it will come easily to you.

Number 1: Two angles given plus any side = SINE RULE needed

Number 2: Two sides given plus an angle not enclosed = SINE RULE needed

For the example above there is still more to do. You need to do sin-1(0.36) =21.1° which is the answer!

Please note for this example I have already rearranged the sine rule. I have flipped the formula so that the angles 'A' and 'B' are on the top of the formula and 'a' and 'b' are on the bottom.

Number 3: Two sides given plus the angle enclosed = COSINE RULE needed

Please note here that I have used the 'normal' form of the cosine rule.

Number 4: All three sides given but no angles = COSINE RULE needed

Please note that here I have used the rearranged version of the cosine rule.

These are four examples of the ways you can use the sine and cosine rule. This is a grade A topic.

PRACTICE QUESTIONS

Q1- Find the side x in each question. Give your answer correct to 1 decimal place.

a)

b)

Q2- Find the angle x. Give your answer to the nearest degree.

c)

Q3- Find x or θ in each case

d)

e)

f)

g)

ANSWERS



a)

b)

c)

I have not yet worked out the answers to d, e, f, and g but when I have I will insert them below!

Amelia :)