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2 years ago

Assume that theta is a positive acute angle.

Mathematics

1 answer:

muminat2 years ago

6 0

Answer:

Step-by-step explanation:sin

(

)

Use the definition of sine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

sin

(

)

opposite

hypotenuse

Find the adjacent side of the unit circle triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.

Adjacent

√

hypotenuse

−

opposite

Replace the known values in the equation.

Adjacent

√

(

)

−

(

)

Simplify

√

(

)

−

(

)

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Adjacent

Find the value of cosine.

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cos

(

)

Find the value of tangent.

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tan

(

)

Find the value of cotangent.

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cot

(

)

Find the value of secant.

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sec

(

)

Find the value of cosecant.

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csc

(

)

This is the solution to each trig value.

sin

(

)

cos

(

)

tan

(

)

cot

(

)

sec

(

)

csc

(

)

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3 years ago

Use the following triangle to find Sec theta.

makkiz [27]

Answer:

$\frac{\sqrt{41}}{4}$

Step-by-step explanation:

sec(theta) is defined as: $sec(\theta)=\frac{1}{cos(\theta)} = \frac{hypotenuse}{adjacent}$

In the diagram you provided the hypotenuse of the triangle is sqrt(41) and the opposite side is 5, using these two sides, we can solve for the adjacent side by using the Pythagorean Theorem: $a^2+b^2=c^2$

So this gives us the equation where a=adjacent side:

$a^2+5^2=\sqrt{41}^2$

$a^2+25=41$

Subtract 25 from both sides

$a^2=16$

Take the square root of both sides

$a=4$

So now plug this into the definition of sec(theta) and you get: $\frac{\sqrt{41}}{4}$ . This is in most simplified form since 41, has no factors besides 41 and 1.

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2 years ago