C2 Trigonometry

Could someone please help me with this question!

Solve,for 0<x<180,the equation (The interval should be less than or equal to)

(a) cos 2x=-0.9,giving your answers to 1 decimal place

Thanks............................. :smile:

Reply 1

Dekota

vaider

Solve,for 0<x<180,the equation

(a) cos 2x=-0.9, 1.d.p

Use identity (cos 2x = 1 - 2sin²x) ..

cos 2x = 1 - 2sin²x -0.9
......... = 1.9/2 = sin²x
......... = √(19/20) = sinx
......... = arcsin√(19/20) = x
......... x ≈ 77.1°, 257.1° etc.

Reply 2

vaider

OP

You dont use an identity you simply have to uses quadrants,from the calculation of x.Where in the first quadrant all are positive,second quadrant sin is positve and so on................................................

Reply 3

Dekota

vaider

You dont use an identity you simply have to uses quadrants,from the calculation of x.Where in the first quadrant all are positive,second quadrant sin is positve and so on................................................

yes but the question has cos [2x], the normal way cannot be used as with cosx. You have to change it to end up with only x.

If you know another way .. then do that, but I don't think there is one. :smile:

Reply 4

Dekota

vaider

You dont use an identity you simply have to uses quadrants,from the calculation of x.Where in the first quadrant all are positive,second quadrant sin is positve and so on................................................

Oh okay .. heres the answer without use of identity:

cos 2x = -0.9
.......x = ½arccos[-0.9]
......... x ≈ 77.1° etc. ... e.g 180 - 77.1 = 102.9°

C2 Trigonometry

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