You are Here: Home >< Maths

# Simplifying trigonometric ratios Watch

1. I'm doing a few exercises where you need to simplify trigonometric ratios of either 30, 45 to 60 degrees

Here are the examples it gave.

cos(405)
cos(405) = cos(360+45)
=cos(45)

tan(120)
tan(120) = tan(180-60)
=tan(-60)
=-tan(60)

sin(300)
sin(300)=sin(360-60)
=sin(-60)
=-sin(60)

so it seems that the rules are
sin(-x) = -sin(x), cos(-x) = -cos(x), tan(-x) = -tan(x)
sin(360+x) = sin(-360+x) = sin(x)
cos(360+x) = cos(-360+x) = cos(x)
tan(180+x) = tan(-180+x) = tan(x)

Let's say you have
cos(-210)
adding 360 won't help you in any way as you will just be left with cos(150) and the examples never bothered to show how to handle this situation. but I think you can just add or remove 180 and flip the sign

cos(-210)= -cos(-210 + 180) = -cos(-30)
= --cos(30) = cos(30), but this is wrong. So "cos(-x) = -cos(x)" does not always work. Are there any consistent rules for how to simplify these? The ones the example is showing don't even work.
2. (Original post by Bobby132)
I'm doing a few exercises where you need to simplify trigonometric ratios of either 30, 45 to 60 degrees

Here are the examples it gave.

cos(405)
cos(405) = cos(360+45)
=cos(45)

tan(120)
tan(120) = tan(180-60)
=tan(-60)
=-tan(60)

sin(300)
sin(300)=sin(360-60)
=sin(-60)
=-sin(60)

so it seems that the rules are
sin(-x) = -sin(x), cos(-x) = -cos(x), tan(-x) = -tan(x)
sin(360+x) = sin(-360+x) = sin(x)
cos(360+x) = cos(-360+x) = cos(x)
tan(180+x) = tan(-180+x) = tan(x)

Let's say you have
cos(-210)
adding 360 won't help you in any way as you will just be left with cos(150) and the examples never bothered to show how to handle this situation. but I think you can just add or remove 180 and flip the sign

cos(-210)= -cos(-210 + 180) = -cos(-30)
= --cos(30) = cos(30), but this is wrong. So "cos(-x) = -cos(x)" does not always work. Are there any consistent rules for how to simplify these? The ones the example is showing don't even work.
cos(-x)=cos(x)
3. (Original post by Bobby132)
I'm doing a few exercises where you need to simplify trigonometric ratios of either 30, 45 to 60 degrees

Here are the examples it gave.

cos(405)
cos(405) = cos(360+45)
=cos(45)

tan(120)
tan(120) = tan(180-60)
=tan(-60)
=-tan(60)

sin(300)
sin(300)=sin(360-60)
=sin(-60)
=-sin(60)

so it seems that the rules are
sin(-x) = -sin(x), cos(-x) = -cos(x), tan(-x) = -tan(x)
sin(360+x) = sin(-360+x) = sin(x)
cos(360+x) = cos(-360+x) = cos(x)
tan(180+x) = tan(-180+x) = tan(x)

Let's say you have
cos(-210)
adding 360 won't help you in any way as you will just be left with cos(150) and the examples never bothered to show how to handle this situation. but I think you can just add or remove 180 and flip the sign

cos(-210)= -cos(-210 + 180) = -cos(-30)
= --cos(30) = cos(30), but this is wrong. So "cos(-x) = -cos(x)" does not always work. Are there any consistent rules for how to simplify these? The ones the example is showing don't even work.
4. Rather than trying to learn rules that you are not even sure of it would be better to use the graphs or the CAST diagram

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: April 14, 2012
Today on TSR

### Should I ask for his number?

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

## Make your revision easier

### 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

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE