The angle θ1\theta_1 θ 1 theta, start subscript, 1, end subscript is located in Quadrant II\text{II} II start text, I, I, end text , and cos⁡(θ1)=−211\cos(\theta_1)=-\dfrac {2}{11} cos(θ 1 )=− 11 2 cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, minus, start fraction, 2, divided by, 11, end fraction . What is the value of sin⁡(θ1)\sin(\theta_1) sin(θ 1 ) sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis ?

The sine of an angle θ is positive in quadrant II, and the value of sine θ is

The given parameters are:

Using trigonometry ratio, we have:

Substitute

Evaluate the square

Subtract 4/121 from both sides

Take LCM

Simplify the numerator

Take square roots of both sides

This gives

From the question, we understand that angle θ is located in quadrant II.

The sine of an angle θ is positive in quadrant II

So, we have:

Hence, the value of sine θ is

Read more about quadrants at:

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Step-by-step explanation:

Given that the angle  is located in Quadrant II; and

In Quadrant II, x is negative and y is positive.

To find , we first determine the opposite angle of .

This will be done using the Pythagoras theorem.

Therefore:

4 & 3

step-by-step explanation:

factor of 108=2×2×3×3×3=2×2×3^3=the number is 4 because 2 only occurs 2 times and 2×2=4 and factor of 2187=3^3×3^3×3=the number is 3 because 3 onlyvoccur 1 time.

answer: 1 and 3

step-by-step explanation: