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dexar [7]
3 years ago
5

Use a sum or difference identity to evaluate. sin15∘

Mathematics
1 answer:
DIA [1.3K]3 years ago
5 0
Don’t open that link it’s takes all your information
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Angle (theta) is in standard position. If (8,-15) is on the terminal ray of angle (theta), find the values of the trigonometric
mariarad [96]

Answer:

\sin \theta =\frac{-15}{17}\\cos \theta =\frac{8}{17}\\\tan  \theta =\frac{-15}{8}\\\csc \theta =\frac{-17}{15}\\\sec \theta =\frac{17}{8}\\\cot \theta =\frac{-8}{15}

Step-by-step explanation:

Given: (8,-15) is on the terminal ray of angle

To find: All the trigonometric ratios

Solution:

Trigonometry is a  branch of mathematics that explain relationship between the sides and angles of triangles.

If (x, y) lies on the terminal side of  θ  then r=\sqrt{x^2+y^2}

r=\sqrt{(8)^2+(-15)^2}=\sqrt{64+225}=\sqrt{289}=17 units

\sin \theta =\frac{y}{r}=\frac{-15}{17}\\cos \theta =\frac{x}{r}=\frac{8}{17}\\\tan  \theta =\frac{y}{x}=\frac{-15}{8}\\\csc \theta =\frac{1}{\sin \theta }=\frac{-17}{15}\\\sec \theta =\frac{1}{cos \theta}=\frac{17}{8}\\\cot \theta =\frac{1}{\tan  \theta}=\frac{-8}{15}

6 0
3 years ago
A positive real number is 2 less than another. When 4 times the larger is added to the square of the smaller, the result is 49.
Kobotan [32]

Answer:

The numbers are

-2+3\sqrt{5}   and 3\sqrt{5}

Step-by-step explanation:

Let

x -----> the smaller positive real number

y -----> the larger positive real number

we know that

A positive real number is 2 less than another

so

x=y-2

y=x+2 ----> equation A

When 4 times the larger is added to the square of the smaller, the result is 49

so

4y+x^2=49 ----> equation B

substitute equation A in equation B

4(x+2)+x^2=49

solve for x

x^2+4x-41=0

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

x^2+4x-41=0

so

a=1\\b=4\\c=-41

substitute in the formula

x=\frac{-4\pm\sqrt{4^{2}-4(1)(-41)}} {2(1)}

x=\frac{-4\pm\sqrt{180}} {2}

x=\frac{-4\pm6\sqrt{5}} {2}

x=-2\pm3\sqrt{5}

so

The positive real number is

x=-2+3\sqrt{5}

Find the value of y

y=x+2

y=-2+3\sqrt{5}+2

y=3\sqrt{5}

6 0
3 years ago
THIS is due in a hour Justin gave the waiter a $2.25 tip at the restaurant. If his meal cost $12.50, what percent tip did he giv
polet [3.4K]
2.25/12.50 = 0.18. then turn 0.18 into a percentage by doing 0.18 x 100 = 18%. Therefore, he gave an 18% tip.
3 0
2 years ago
Read 2 more answers
in parallelogram ABCD, AC is diagonal, the measure <ABC is 40°, and the measure of <ACD IS 57°. what is the measure of &lt
Nutka1998 [239]

Answer: \angle CAD = 83^\circ Option D


Step-by-step explanation:

In this question we use properties of parallelogram and angle sum property of a triangle.

In parallelogram ABCD


\angle ABC=40^\circ


As, we know that opposite angles of parallelogram are equal


Therefore,


\angle ABC =\angle ADC =40^\circ


Now, in triangle ADC

We know that sum of all the angles of a triangle is =180^\circ


\angle ACD +\angle ADC +\angle DAC =180^\circ


57^\circ +40^\circ +\angle DAC =180^\circ


97^\circ + \angle DAC = 180^\circ

Subtracting 97 from both sides we get


\angle DAC = 180^\circ - 97^\circ


\angle DAC = 83^\circ


Measure of \angle CAD = 83^\circ


3 0
3 years ago
How does the graph y=3^x compare to the graph y=3^-x
LUCKY_DIMON [66]

Answer:

Y = 3x^x is a graph that has exponential growth while y = 3^-x has exponential decay.

Y = 3x^x (-∞, 0) and (∞, ∞).

Y = 3x^-x (-∞, ∞) and (∞, 0).

Step-by-step explanation:

The infinity symbols were being used to represent the x and y values of each graph. I will call y = 3^x "graph 1" and y = 3^-x "graph 2".

When graph 1 had positive ∞ for its x value, its y value was reaching towards positive ∞. When its x was reaching for negative ∞, its y was going for 0.

For graph 2, however, when its x was reaching for positive ∞, its x was reaching for 0. When its x was reaching for negative ∞, its y was going for positive ∞.

Here's an image of the graphs:

5 0
2 years ago
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