A. Name 3 different angles which could have a reference angle of 20 degrees. How did you arrive at this answer?.

Mathematics

1 answer:

IgorC [24]3 years ago

8 0

Answer:

Answer:a. Since 20° is in the first quadrant, the reference angle is 20° .

Answer:a. Since 20° is in the first quadrant, the reference angle is 20° .b. Reference Angle: the acute angle between the terminal arm/terminal side and the x-axis. The reference angle is always positive. In other words, the reference angle is an angle being sandwiched by the terminal side and the x-axis. It must be less than 90 degree, and always positive.c. The rays corresponding to supplementary angles intersect the unit circles in points having the same y-coordinate, so the two angles have the same sine (and opposite cosines).

hopefully,

Zara♡

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Find the exact value of the following, without using a calculator.

bekas [8.4K]

9514 1404 393

Answer:

(√17 -4√595)/102

Step-by-step explanation:

To use the sine of the angle sum formula, we need to know the sine and cosine of each of the angles.

sin(sin^-1(1/6)) = 1/6 . . . . a first-quadrant angle

cos(sin^-1(1/6)) = √(1 -(1/6)²) = √(35/36) = (√35)/6

sin(tan^-1(-4)) = -4/√(1+(-4)²) = -4/√17 . . . . a 4th-quadrant angle

cos(tan^-1(-4)) = √(1 -(-4/√17)²) = 1/√17

The sum of angles formula is ...

sin(α+β) = sin(α)cos(β) +cos(α)sin(β)

So, our sine is ...

$\sin\left(\sin^{-1}\left(\dfrac{1}{6}\right)+\tan^{-1}(-4)\right)=\dfrac{1}{6}\cdot\dfrac{1}{\sqrt{17}}+\dfrac{\sqrt{35}}{6}\cdot\dfrac{-4}{\sqrt{17}}\\\\=\dfrac{1-4\sqrt{35}}{6\sqrt{17}}=\boxed{\dfrac{\sqrt{17}-4\sqrt{595}}{102}}$