Senior 1 Mathematics Compulsory 4 Trigonometric Functions

If cos(+a) = -1 2

Then +a= 3+ or +a=2 3a= 3, due to the periodicity of trigonometric functions: a= 3+2n , n is an integer.

Therefore, sin(2+a)=12

f(x)=sinx+sin( 2-x)=sinx+cosx=root number 2sin(x+4).

So the period t=2 and the maximum value is.

Root number 2, the minimum value is negative root number 2

f（a)=3/4=sina+cosa

Sin2 (squared) a+cos 2a = 1, (sina + cosa) 2 = 9 16 = 1 + sin2a to obtain sin2a = 7 16

Question 2: f(x)=4sin(x-6), so the maximum value is f(2 3)=4, and the minimum value f(0)=-2

f(x)=0 gives x= 6

Original = (cosx-sinx) (sinx+cosx) = 2 - root number 3

cos（π+a）= -cosa=-1/2

cosa=1/2

sin( 2 + a) = cosa=1 2 formula can be memorized.

To prove, it is only necessary to know the trigonometric symbols of the four quadrant angles.

For sine, the quadrant with a positive sign is 1

For cosine, the elephant cherry stool with a positive sign is limited to 1

For tangents and cotangents, the coarse quadrant with a positive sign is 1

Then it is not difficult to understand the above conclusion.

From left to right, it is not difficult to prove, from omitted!

From right to left. 1) When the product of sine and tangent is negative, it means that the signs of sine and tangent are different, and 1 quadrant is positive.

All 4 quadrants are negative.

Only the 23 quadrants of the spine are one positive and one negative.

2) Similar, omitted.

The conditions are squared on both sides.

sina)^2+(cosa)^2+2sinacosa=1/251+2sinacosa=1/25

sinacosa=-12/25

sina+cosa=1/5

sina, cosa is the root of x 2-(1 5) x-12 25 = 0 cosa = -3 5, sina = 4 5 or sina = -3 5, cosa = 4 5, tana = sina cosa = -4 3 or -3 4

Let sina = 1-cos 2a = t

The solution yields t = -3 5 or 4 5

i.e. sina = -3 5 or 4 5

cosa = 4 5 or -3 5

Get tana = -3 4

or -4 3

(sina + cosa) 2 = 1 25 and combined with sina 2 + cosa 2 = 1.

2sinacosa = -24 25, divide the left and right sides by 1 at the same time, and approximate cosa 2 to get :

tana (tana 2+1) = -12 25, get:

12tana^2+25tana+12=0

Get tana = -3 4 or -4 3

Both are on topic.

Key: The magic of 1.

Left and right are the same square, that is, sina 2 + 2 sinacosa + cosa 2 = 1 25

2sinacosa=-24/25

There is a universal formula (both the left side and the top and bottom are divided by cosa 2).

2tana (1+tana 2)=-24 25 results are out.

By sinx 0, 2k x 2k+

By 1-tanx 0, get k - 22k, 2k + dannian 4], [2k + 2, 2k +

k is an integer) from sinx 0 to get 2k x 2k + from 1-tanx to get k - 2 turns out wrong? Sidelines???

From the value of x, we know that cos2x is less than zero, and we put sinx+cosx=1 5 squares, and there are 1+2sinxcosx=1 25, which is sin2x=-24 25, so cos2x=7 25

f(x)=cos2x+2sinx

2cos^2 x -1 + 2sinx

1- 2sin^2 x + 2sinx

2(sinx - 1 2) 2 + 3 2 The most guessed small value is -2(-1-1 2) 2 + 3 2 = 3 The maximum value of spike contains 3 2

It is necessary to use a quadratic function to solve the problem in the form of a quadratic function.

1.Original formula (cos 4cos sin 4sin ) 2 (cos 4cos -sin 4sin ) 2=1 2(cos 2 sin 2 2cos sin ) 1 2(cos 2 sin 2 2cos sin )=1 2 1 2=1 The second question is also equal to 1

It's so easy to take out and dry.