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3 years ago

7

What are all the exact solutions of 2sec^2x-tan^4x=-1 ?

1 answer:

Nataly_w [17]3 years ago

8 0

The first thing to do would be to simplify the equation first. Let's apply the trigonometric functions properties where 1 + tan²x = sec² x. So, we can substitute this to the equation so that it would purely be a function of tangents.

<span>2sec</span>²<span>x-tan</span>⁴<span>x=-1
2(1+tan</span>²x) - tan⁴x = 1
2 + 2 tan²x - tan⁴x + 1 = 0
tan⁴x - 2tan²x + 1 = 0
(tanx -1)² = 0
tanx - 1 = 0
tanx = 1
x = tan⁻¹ 1
x = 45°

So, the solution for the given trigonometric equation is 45° or π/4 radians.

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Calculate the measure of the major arc MPN.

34kurt

Answer:

310°

Step-by-step explanation:

The sum of arcs around a circle is 360°.

MPN +MN = 360°

MPN = 360° -MN . . . . . . . . subtract MN

MPN = 360° -50° = 310° . . . fill in the given value

The measure of major arc MPN is 310°.

4 0

2 years ago

Please help me! DO NOT SEND LINK!

svet-max [94.6K]

Answer:

<u>So option 4; </u> $\frac{35}{100}$ <u> is the correct option</u>

Step-by-step explanation:

First, we need to convert $\frac{2}{10}$ so it's denominator is 100. To do so, we will multiply the numerator and denominator by 10

$\frac{2}{10} *\frac{10}{10} = \frac{20}{100}$

Second, we need to add the two fractions to get the current total distance walked. Remember, when adding fractions, the denominator does not change.

$\frac{45}{100} + \frac{20}{100} = \frac{65}{100}$

Now that we have the total distance walked, we need to subtract that to 1 mile. $1mile=\frac{1}{1} = \frac{10}{10} =\frac{100}{100}$

$\frac{100}{100} -\frac{65}{100} = \frac{35}{100}$

So option 4; $\frac{35}{100}$ is the correct option

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3 years ago

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