MATHEMATICS HIGH SCHOOL

Ya) Match the graph shown with one of the following equations.
y = x + 2
y=-x-2
y = x-2
y = -x + 2
y = -X
A
B
C
D
E
O
х
b) Which one of the following points lies on the line 3y = 2x - 1?
(2,6) (1,2) (2, 1) (-2, 1) (2,-6)
A
B
C
D
E
y a) Match the graph shown with one of the - 1

Answers

Answer 1
Answer:

Answer:

See attachment.

a)  y = -x + 2

b)  (2,1)

Step-by-step explanation:

Explained in the attachment.

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Step-by-step explanation:

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What is the value of cos(x/2) if tan x=1/2 and x is in quadrant III

Answers

The value of cos(x/2) is required.

The required value is \cos(x/2)=-\sqrt{(5-2√(5))/(10)}

Trigonometry

The given value is

\tan x=(1)/(2) where x is in quadrant III.

From trigonometricidentities we have

\sec^2x=1+\tan^2x\n\Rightarrow \sec^2x=1+((1)/(2))^2\n\Rightarrow \sec^2x=(5)/(4)\n\Rightarrow \cos^(2)x=(4)/(5)\n\Rightarrow \cos x=(2)/(√(5))

If x lies in quadrant III then x/2 lies in quadrant II.

Cos is negative in quadrantIII so,

\cos x=-(2)/(√(5))=-(2√(5))/(5)

\cos (x)/(2)=\pm \sqrt{(1+\cos x)/(2)}\n =\pm\sqrt{(1-(2√(5))/(5))/(2)}\n =\pm\sqrt{(5-2√(5))/(10)}

Since, x/2 lies in the secondquadrant and cos (x/2) is negative.

The required value is -\sqrt{(5-2√(5))/(10)}

Learn more about trigonometry:

brainly.com/question/24349828

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