Given that a is an acute angle and COS (a + 45 degrees) = 3 / 5, find cosa =?

Given that a is an acute angle and COS (a + 45 degrees) = 3 / 5, find cosa =?

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Given that α∈ (60 °, 90%), sin (α - 30 °) = 3 / 5, find the value of cos α

α∈（60º,90º）
α-30º∈（30º,60º）
So cos (α - 30 & # 186;) = 4 / 5
cosα=cos[(α-30)+30]=cos(α-30)cos30-sin(α-30)sinα=4/5*√3/2-3/5*1/2=(4√3-3)/10

Cos (a + 30) = 0.6 (0,90) for cosa

cos(a+30)=0.6 ->sin(a+30)=0.8
->cosa=cos(a+30-30)=cos(a+30)cos30+sin(a+30)sin30=0.6*0.866+0.8*0.5
=0.9196

It is known that cosa = - 4 / 5, a belongs to (180 ° and 270 °), Tan, v = - 1 / 3, V belongs to (90 ° and 180 °) and COS (a + V) =?
How to find cos v?

A in the third quadrant
sina0,cosb

Given cos (θ + 30 degrees) = 5 / 13, θ belongs to (0,90 degrees), find cos θ
I just mentioned this, but the two answers are different

So sin (θ + 30) > 0sin & sup2; (θ + 30) + cos & sup2; (θ + 30) = 1, so sin (θ + 30) = 12 / 13, so cos θ = cos [(θ + 30) - 30] = cos (θ + 30) cos30 + sin (θ + 30) sin30 = 5 / 13 * √ 3

If Tan (π + a) = 2, then (2sina + COSA) / (sina-3cosa)=

tan（π+a）=2
Using the induction formula Tana = 2
(2sina+cosa)/(sina-3cosa)
The numerator and denominator are divided by cosa at the same time
=(2tana+1)/(tana-3)
=(2*2+1)/(2-3)
=-5

Given Sina + 3cosa = 0, then the quadrant of a is

Because Sina + 3cosa = 0
So Sina = - 3cosa
Substitute Sina ^ 2 + cosa ^ 2 = 1 to get cosa ^ 2 = 1 / 10
(sina+3cosa)^2=0
sina^2+6sinacosa+9cosa^2=0
8cosa^2+3sin2a+1=0
Then sin2a = - 3 / 5
∏＋2k∏＜2a＜2∏+2k∏
∏/2+∏＜a＜∏+k∏(k∈Z)
So a is in the second, fourth quadrant

Solving sina-3cosa / Sina + 3cosa given sina-2cosa = 0
Find Sin & # a + sinacosa + 3

sina-2cosa=0
sina=2cosa
sina-3cosa/sina+3cosa
=2cosa-3cosa / 2cosa+3cosa
=-cosa/5cosa
=-1/5

sina+3cosa=0
Then sin (π + a) cos (π - a)=

sina+3cosa=0
Sina = - 3cosa substituting (Sina) ^ 2 + (COSA) ^ 2 = 1
So (COSA) ^ 2 = 1 / 10
Induction formula
sin(π+a)cos(π-a)
=(-sina)(-cosa)
=sinacosa
=-3cosa*cosa
=-3/10

The terminal point P (- 5m, 12m) (m) of known angle a

According to the definition of trigonometric function: r = OP = √ [(- 12m) ² + (5m) ²] = 13|m|
sinα=y/r,cosα=x/r
∵m