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4 years ago

63 to 28 in simplest form

Mathematics

2 answers:

ser-zykov [4K]4 years ago

8 0

Answer:

it's already in the simplest form

Step-by-step explanation:

sergij07 [2.7K]4 years ago

5 0

Answer:

63 to 28

Step-by-step explanation:

it is already in simplest form

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Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.

notsponge [240]

ANSWER

$\sin( \theta) = - \frac{15}{17}$

$\csc( \theta) = - \frac{17}{15}$

$\cos( \theta) = \frac{8}{17}$

$\sec( \theta) = \frac{17}{8}$

$\tan( \theta) = - \frac{15}{8}$

$\cot( \theta) = - \frac{8}{15}$

EXPLANATION

From the Pythagoras Theorem, the hypotenuse can be found.

${h}^{2} = 1 {5}^{2} + {8}^{2}$

${h}^{2} = 289$

$h = \sqrt{289}$

$h = 17$

The sine ratio is negative in the fourth quadrant.

$\sin( \theta) = - \frac{opposite}{hypotenuse}$

$\sin( \theta) = - \frac{15}{17}$

The cosecant ratio is the reciprocal of the sine ratio.

$\csc( \theta) = - \frac{17}{15}$

The cosine ratio is positive in the fourth quadrant.

$\cos( \theta) = \frac{adjacent}{hypotenuse}$

$\cos( \theta) = \frac{8}{17}$

The secant ratio is the reciprocal of the cosine ratio.

$\sec( \theta) = \frac{17}{8}$

The tangent ratio is negative in the fourth quadrant.

$\tan( \theta) = - \frac{opposite}{adjacent}$

$\tan( \theta) = - \frac{15}{8}$

The reciprocal of the tangent ratio is the cotangent ratio

$\cot( \theta) = - \frac{8}{15}$

8 0

3 years ago

Read 2 more answers

Use the diagram of point O. What is the length of OY to the nearest 10th of an Inch? XZ = 10 and OX= 10

Lady bird [3.3K]

From the diagram above,

XZ = 10 in and OX = 10 in

we are to find length of OY

XZ is a chord and line OY divides the chord into equal length

Hence, ZY=YX= 5 in

Now we solve the traingle OXY

To find OY we solve using pythagoras theorem

$(Hyp)^2=(Opp)^2+(Adj)^2$

applying values from the triangle above

$\begin{gathered} OX^2=XY^2+OY^2 \\ 10^2=5^2+OY^2 \\ 100=25+OY^2 \\ OY^2\text{ = 100 -25} \\ OY^2\text{ = 75} \\ OY\text{ = }\sqrt[]{75} \\ OY\text{ = }\sqrt[]{25\text{ }\times\text{ 3}} \\ OY\text{ = 5}\sqrt[]{3\text{ }}in \end{gathered}$

Therefore,

Length of OY =

$5\sqrt[]{3}$

8 0

1 year ago

Two points are located on a rigid wheel that is rotating with an increasing angular velocity about a fixed axis. The axis is per

exis [7]

Answer:

Same angular velocity

Same angular acceleration

Point 1 has greater tangential speed

Point 1 has greater tangential acceleration

Point 1 has greater centripetal acceleration

Step-by-step explanation:

Since both points are located on the rigid wheel, their angular velocity and acceleration must be the same for all point located on the wheel.

The tangential quantities, however, would depend on how far they are from the axis of rotation:

$v = \omega R$

$a_T = \alpha R$

$a_c = \omega^2 R$

where $\omega, \alpha$ are the angular velocity and acceleration, respectively, which is the same for 2 points. R is the radius of rotation. In this case point 1 has a larger radius since it lies on the rim and point 2 is only half way between.