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# Any tips of solving Simplify, verify and prove?

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I feel so bad when solving these types of question.(sin cos tan sec csc cot)

XavierZz  Dec 9, 2015

#1
+92437
+10

I feel so bad when solving these types of question.(sin cos tan sec csc cot)

Hi XavierZz

Lets see

Reciprocal ratios

cot=1/tan         see how the 3rd letter in the less familiar one = the first letter in the 'normal' one

sec=1/cos        see the 3rd/1st leter thing again

cosec=1/sin     and  again  (in Australia we write cosec not just csc

Complementary ratios

Remember: Complementary angels add up to 90 degrees

$$cosine\theta=sine(90-\theta) \;and\; vise\; versa \\ cotangent\theta=tangent(90-\theta) \;and\; vise\; versa \\ cosec \theta=sec(90-\theta) \;and\; vise\; versa \\$$

The 'co' stands for complimentary.

Identities that you need to remember are

$$\\~\\ \boxed{cos^2\theta+sin^2\theta=1\\~\\ sin(x+y)=sinxcosy+cosxsiny\\~\\ cos(x+y)=cosxcosy-sinxsiny\\}$$

Just about everything else can be worked out from there.

I don't think I remember anything much else but most people remember a few more because it takes them too long or it is too difficult for them to derive other things.

NOW IT IS JUST A MATTER OF PRACTICE, PRACTICE AND MORE PRACTICE.

Melody  Dec 9, 2015
edited by Melody  Dec 9, 2015
edited by Melody  Dec 9, 2015
edited by Melody  Dec 9, 2015
edited by Melody  Dec 9, 2015
edited by Melody  Dec 9, 2015
edited by Melody  Dec 9, 2015
Sort:

#1
+92437
+10

I feel so bad when solving these types of question.(sin cos tan sec csc cot)

Hi XavierZz

Lets see

Reciprocal ratios

cot=1/tan         see how the 3rd letter in the less familiar one = the first letter in the 'normal' one

sec=1/cos        see the 3rd/1st leter thing again

cosec=1/sin     and  again  (in Australia we write cosec not just csc

Complementary ratios

Remember: Complementary angels add up to 90 degrees

$$cosine\theta=sine(90-\theta) \;and\; vise\; versa \\ cotangent\theta=tangent(90-\theta) \;and\; vise\; versa \\ cosec \theta=sec(90-\theta) \;and\; vise\; versa \\$$

The 'co' stands for complimentary.

Identities that you need to remember are

$$\\~\\ \boxed{cos^2\theta+sin^2\theta=1\\~\\ sin(x+y)=sinxcosy+cosxsiny\\~\\ cos(x+y)=cosxcosy-sinxsiny\\}$$

Just about everything else can be worked out from there.

I don't think I remember anything much else but most people remember a few more because it takes them too long or it is too difficult for them to derive other things.

NOW IT IS JUST A MATTER OF PRACTICE, PRACTICE AND MORE PRACTICE.

Melody  Dec 9, 2015
edited by Melody  Dec 9, 2015
edited by Melody  Dec 9, 2015
edited by Melody  Dec 9, 2015
edited by Melody  Dec 9, 2015
edited by Melody  Dec 9, 2015
edited by Melody  Dec 9, 2015