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3 years ago

PLEASE HELP Trig Idenities

Mathematics

1 answer:

kari74 [83]3 years ago

4 0

$\dfrac{\sin(A+B)}{\sin(A-B)}=\dfrac{\sin A\cos B+\cos A\sin B}{\sin A\cos B-\cos A\sin B}$

Divide through all terms by $\cos A\cos B$ . Then, for instance, the first term in the numerator becomes

$\dfrac{\sin A\cos B}{\cos A\cos B}=\dfrac{\sin A}{\cos A}=\tan A$

All other terms reduce similarly, giving the final product

$\dfrac{\tan A+\tan B}{\tan A-\tan B}$

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PLZ HURRY IT'S URGENT!!

Ksenya-84 [330]

The answer would be 40
-4(-2) = 8
8(5) = 40

7 0

3 years ago

Find the product. Write your answer in scientific notation. (3 x 10^2)×(4×10^5)

suter [353]

Answer:

12 * 10 ^ 7

Step-by-step explanation:

3 * 10 ^ 2 * 4 * 10 ^5

= 12 * 10^ 2 + 5

= 12 * 10 ^ 7

Hope it will help :)

7 0

3 years ago

In this equation you have to solve for x

lidiya [134]

Answer:

Step-by-step explanation:

tan 36° = x/40

x = 40 * tan 36°

x ≈ 29.1

6 0

2 years ago

Which number comes first if the numbers 2.001, 0.0035, 0.0005, 4.56094 are arranged in order from most to fewest significant dig

Verizon [17]

D. comes first as it has the most significant figures. Hope this helps!!

8 0

3 years ago

Please help w this! Its a calculus question! look at the picture for the problem,

neonofarm [45]

Since you mentioned calculus, perhaps you're supposed to find the area by integration.

The square is circumscribed by a circle of radius 6, so its diagonal (equal to the diameter) has length 12. The lengths of a square's side and its diagonal occur in a ratio of 1 to sqrt(2), so the square has side length 6sqrt(2). This means its sides occur on the lines $x=\pm3\sqrt2$ and $y=\pm3\sqrt2$ .

Let $R$ be the region bounded by the line $x=3\sqrt2$ and the circle $x^2+y^2=36$ (the rightmost blue region). The right side of the circle can be expressed in terms of $x$ as a function of $y$ :

$x^2+y^2=36\implies x=\sqrt{36-y^2}$

Then the area of this circular segment is

$\displaystyle\iint_R\mathrm dA=\int_{-3\sqrt2}^{3\sqrt2}\int_{3\sqrt2}^{\sqrt{36-y^2}}\,\mathrm dx\,\mathrm dy$

$=\displaystyle\int_{-3\sqrt2}^{3\sqrt2}(\sqrt{36-y^2}-3\sqrt2)\,\mathrm dy$

Substitute $y=6\sin t$ , so that $\mathrm dy=6\cos t\,\mathrm dt$

$=\displaystyle\int_{-\pi/4}^{\pi/4}6\cos t(\sqrt{36-(6\sin t)^2}-3\sqrt2)\,\mathrm dt$

$=\displaystyle\int_{-\pi/4}^{\pi/4}(36\cos^2t-18\sqrt2\cos t)\,\mathrm dt=9\pi-18$

Then the area of the entire blue region is 4 times this, a total of $\boxed{36\pi-72}$ .

Alternatively, you can compute the area of $R$ in polar coordinates. The line $x=3\sqrt2$ becomes $r=3\sqrt2\sec\theta$ , while the circle is given by $r=6$ . The two curves intersect at $\theta=\pm\dfrac\pi4$ , so that

$\displaystyle\iint_R\mathrm dA=\int_{-\pi/4}^{\pi/4}\int_{3\sqrt2\sec\theta}^6r\,\mathrm dr\,\mathrm d\theta$

$=\displaystyle\frac12\int_{-\pi/4}^{\pi/4}(36-18\sec^2\theta)\,\mathrm d\theta=9\pi-18$

so again the total area would be $36\pi-72$ .

Or you can omit using calculus altogether and rely on some basic geometric facts. The region $R$ is a circular segment subtended by a central angle of $\dfrac\pi2$ radians. Then its area is

$\dfrac{6^2\left(\frac\pi2-\sin\frac\pi2\right)}2=9\pi-18$

so the total area is, once again, $36\pi-72$ .

An even simpler way is to subtract the area of the square from the area of the circle.

$\pi6^2-(6\sqrt2)^2=36\pi-72$

6 0

3 years ago