You are Here: Home >< Maths

1. A trigonometric function of a number is given below. Without calculator, find all the other numbers x, 0 ≤ x ≤ 360, such that the same function of x is equal to the given trigonometric ratio. E.g. if you're given sin 80°, then x = 100°, since sin 100° = sin 80°

g) sin 400°
h) cos(-30°)
j) sin(-260°)
k) cos(-200°)
2. draw a sine graph fairly accurately.

find sin 400° on your graph. draw a horizontal line y = sin 400°

see where it cuts the sine graph between 0° and 360°; relate the x values to the 400° , taking into account symmetry and periodicity.

repeat with cosine graph etc
3. (Original post by osayuki)
A trigonometric function of a number is given below. Without calculator, find all the other numbers x, 0 ≤ x ≤ 360, such that the same function of x is equal to the given trigonometric ratio. E.g. if you're given sin 80°, then x = 100°, since sin 100° = sin 80°

g) sin 400°
h) cos(-30°)
j) sin(-260°)
k) cos(-200°)
Are you familiar with the 'special triangles'?
Would you know cos and sin of 0, 30, 45, 60, 90...?
EDIT: Yikes, I didn't read the question properly.
You can use a graph, or a CAST circle, or some formulas.
4. (Original post by the bear)
draw a sine graph fairly accurately.

find sin 400° on your graph. draw a horizontal line y = sin 400°

see where it cuts the sine graph between 0° and 360°; relate the x values to the 400° , taking into account symmetry and periodicity.

repeat with cosine graph etc
Ok thank you but when I draw a horizontal line it doesn't cross the graph, it just goes along the x axis. Should I draw a vertical line from 400 then a horizontal line?
5. (Original post by EricPiphany)
Are you familiar with the 'special triangles'?
Would you know cos and sin of 0, 30, 45, 60, 90...?
EDIT: Yikes, I didn't read the question properly.
You can use a graph, or a CAST circle, or some formulas.
Thank you, how do I use the CAST circle if the value is negative e.g. sin(-260)?
6. (Original post by osayuki)
Thank you, how do I use the CAST circle if the value is negative e.g. sin(-260)?
Technically you just measure the angle in the opposite direction.
Two ways I can think of doing this:
Either, find the angle 260 and then reflect in the x-axis.
Or, add 360 to the angle until it is positive, -260 + 360 = 100 so find the angle 100. (360 degrees is one full turn, so it brings you back to the same place).
7. (Original post by EricPiphany)
Technically you just measure the angle in the opposite direction.
Two ways I can think of doing this:
Either, find the angle 260 and then reflect in the x-axis.
Or, add 360 to the angle until it is positive, -260 + 360 = 100 so find the angle 100. (360 degrees is one full turn, so it brings you back to the same place).
Thank you!
8. Just visualise or draw the graph and u can see that sin400 is the same value as sin40 and sin140. Do the same for the others

Posted from TSR Mobile
9. CAST is awful. use the graph like i said
10. (Original post by eternaforest)
Just visualise or draw the graph and u can see that sin400 is the same value as sin40 and sin140. Do the same for the others

Posted from TSR Mobile
Thank you
11. Use CAST!
For a value larger than 360, keep adding to it until you get 400. Then whatever you added is your related angle.
For the negative angle instead of going anti-clockwise, go clockwise.
12. (Original post by osayuki)
Thank you
Btw i'm not against CAST at all but I recommend just learning the graphs so you can visualise them in your head and know where the values are the same. It is much more efficient than having to draw the CAST diagram again and again
13. Thank you everyone, I've solved it now

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: December 13, 2015
Today on TSR

Uni league tables

Do they actually matter?

University open days

• University of Exeter
Wed, 24 Oct '18
Wed, 24 Oct '18
• Northumbria University
Wed, 24 Oct '18
Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants