All categories

3 years ago

What are all the exact solutions of -3tan^2x+1=0? Give your answers in radians.

Mathematics

1 answer:

Mazyrski [523]3 years ago

3 0

Answer:

x = ±π/6 +kπ . . . for any integer k

Step-by-step explanation:

Solving for x, we have ...

1 = 3tan(x)² . . . . . add 3tan(x)²

±√(1/3) = tan(x) . . . divide by 3, take the square root

x = arctan(±√(1/3)) +kπ . . . . use the inverse function to find x

x = ±π/6 +kπ

You might be interested in

Need help with this! Due in 10 mins please

svetlana [45]

True for some cases

7 0

3 years ago

Read 2 more answers

For which value of theta is sin theta equals -1?

Olin [163]

Answer:

The value of Ф is 3π/2

Step-by-step explanation:

* Lets revise the angle Ф in the four quadrant

∵ r = √(x² + y²) ⇒ square the two sides

∴ x² + y² = r²

∵ r = 1

∴ x² + y² = 1

∵ cos² Ф + sin² Ф = 1

∵ x is the adjacent side to Ф and y is the opposite side to Ф

∴ x = cos Ф and y = sin Ф

- At point (1 , 0)

∵ x = 1 , y = 0

∴ cos Ф = 1 and sin Ф = 0

∵ The positive part of x-axis represents the angle 0 and 2π

∴ cos 0 and 2π are 1 and sin 0 and 2π are 0

- At point (0 , 1)

∵ x = 0 , y = 1

∴ cos Ф = 0 and sin Ф = 1

∵ The positive part of y-axis represent the angle π/2

∴ cos π/2 is 0 and sin π/2 is 1

- At point (-1 , 0)

∵ x = -1 , y = 0

∴ cos Ф = -1 and sin Ф = 0

∵ The negative part of x-axis represents the angle π

∴ cos π is -1 and sin π is 0

- At point (0 , -1)

∵ x = 0 , y = -1

∴ cos Ф = 0 and sin Ф = -1

∵ The negative part of y-axis represent the angle 3π/2

∴ cos 3π/2 is 0 and sin 3π/2 is 1

* For the value of Ф = 3π/2 is sin Ф = -1

6 0

4 years ago

Read 2 more answers

A tennis racket normally costs

yKpoI14uk [10]

Th sale price of the tennis racket is 32$
Hope this helps you!

3 0

3 years ago

The graph of a non-invertible function passes through the points (- 1, 2), (0, 6) and (3, - 4) How is the inverse of this functi

KATRIN_1 [288]

Answer:

The order of ordered pairs of a function and its inverse reverse. The graph of the inverse of this function passes through the points (2,-1), (6,0), (-4,3).

Explanation:

I just took the test.

8 0

3 years ago

34. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.

skad [1K]

Answer:

The linear equation for the line which passes through the points given as (-1,4) and (5,2), is written in the point-slope form as $y=\frac{1}{3} x-\frac{13}{3}$ .

Step-by-step explanation:

A condition is given that a line passes through the points whose coordinates are (-1,4) and (5,2).

It is asked to find the linear equation which satisfies the given condition.

Step 1 of 3

Determine the slope of the line.

The points through which the line passes are given as (-1,4) and (5,2). Next, the formula for the slope is given as,

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substitute 2&4 for $y_{2}$ and $y_{1}$ respectively, and $5 \&-1$ for $x_{2}$ and $x_{1}$ respectively in the above formula. Then simplify to get the slope as follows,