All categories

2 years ago

Given sec theta=-4/3 and 90°

Mathematics

1 answer:

hoa [83]2 years ago

3 0

Answer:

Option A.

Step-by-step explanation:

It is given secθ = - $\frac{4}{3}$

then cosθ = - $\frac{3}{4}$

Now we know the identity

sinθ = $\sqrt{1-cos^{2}\theta }$

= $\sqrt{1-(-\frac{3}{4} )^{2}}$

= $\frac{\sqrt{7} }{4}$

Now sin2θ = 2sinθcosθ

Now we put the values of cosine and sine in the formula

sin2θ = 2×(- $\frac{3}{4}$ )( $\frac{\sqrt{7}}{4}$ )

= - $\frac{3\sqrt{7}}{8}$

Therefore, option A. is the answer.

You might be interested in

What is the y intercept? f(x)=-2^2+4x-6

den301095 [7]

Answer:

The y intercept is -1

Step-by-step explanation:

the y-intercept is when y = 0

f(0) = -2^2 + 4(0) - 5

f(0) = 4 - 5

f(0) = -1

8 0

2 years ago

Suppose r(t)=costi+sintj+3tk represents the position of a particle on a helix, where z is the height of the particle above the g

Ilia_Sergeevich [38]

a. The $\vec k$ component tells you the particle's height:

$3t=16\implies t=\dfrac{16}3$

b. The particle's velocity is obtained by differentiating its position function:

$\vec v(t)=\dfrac{\mathrm d\vec r(t)}{\mathrm dt}=-\sin t\,\vec\imath+\cos t\,\vec\jmath+3\,\vec k$

so that its velocity at time $t=\frac{16}3$ is

$\vec v\left(\dfrac{16}3\right)=-\sin\dfrac{16}3\,\vec\imath+\cos\dfrac{16}3\,\vec\jmath+3\,\vec k$

c. The tangent to $\vec r(t)$ at $t=\frac{16}3$ is

$\vec T(t)=\vec r\left(\dfrac{16}3\right)+\vec v\left(\dfrac{16}3\right)t$

4 0

2 years ago

A square root of 54<br><img src="https://tex.z-dn.net/?f=%20%5C%5C%2054%20%5Csqrt%7B3%20%20%7D%20" id="TexFormula1" title=" \\ 5

11111nata11111 [884]

What’s the question?

8 0

2 years ago

Jamie had 4/5 of a spool of twine. He then used 1/2 of a spool of twine to make friendship knots. Over. Explain how you know whe

Ganezh [65]

Answer:

Jamie's claims are correct because 3/10 of the spool twine is left over after using 1/2 of the spool twin for friendship knot

Step-by-step explanation:

Full question: He claims to have 3/10 of the original spool of twine leftover.

First, we compare 3/10 with 4/5 - 1/2

The lowest common multiple for2 and 5 is 10.

To write 4/5 as a fraction with common denominator, multiply numerator and denominator by 2

4/5 = (4×2)/(5×2) = 8/10

To write 1/2 as a fraction with a common denominator, multiply denominator and numerator by5

1/2 =(1×5)/(2×5) = 5/0

So we have :

8/10 - 5/10

Since denominators are equal ,we go ahead and subtract

8/10 - 5/10 = (8-5)/10 = 3/10

4 0

2 years ago

A 30 feet ladder is leaning against the wall. The top of the ladder is resting 25 feet on the building. How far is the base of t

g100num [7]

Answer:

16.58 feet

Step-by-step explanation:

a² + b² = c²

Think of this as a right triangle

The hypotenuse is 30, and one of the legs is 25

To find the other leg, subtract the square of the hypotenuse by the square of the given leg

30² - 25² = leg

900 - 625 = 275

Square root the answer to find the length of the missing leg

√275 = 16.583123951777

The leg is 16.58 ft.

6 0

1 year ago