Mathematics, 23.09.2020 18:01 mikego5

WILL GIVE BRAINIEST IF DONE IN 10 MINUTES If sinθ=−1213 and secθ<0 , what are the values of cosθ,tanθ,cscθ,secθ , and cotθ?Show your work.

SHOW YOUR WORK PLEASE.

Answers: 3

Show answers

Answers

$\sin(\theta)=-12/13\text{ and } \csc(\theta)=-13/12\\\cos(\theta)=-5/13\text{ and } \sec(\theta)=-13/5\\\tan(\theta)=12/5\text{ and } \cot(\theta)=5/12$

Step-by-step explanation:

So we know that:

$\sin(\theta)=-12/13\text{ and } \sec(\theta)$

This tells us that our angle θ is in Quadrant III. This is because, recall ASTC. In QI, everything is positive. This is not the case here since sine and secant are both negative.

In QII, only sine is positive. Since sine is negative, θ can't be in QII.

In QIII, only tangent (and cotangent) is positive. All other are negative. So, θ is in QIII.

And just to check, in QIV, only cosine (and secant) is positive. Since we are told that secant is less than 0 (in other words, negative), θ can't be in QIV.

Now that we know that θ is in QIII, we know that sine and cosecant is negative; cosine and secant is negative; and tangent and cotangent is positive.

Now, let's find the ratios. Remember what sine tells us. Sine gives us the ratio of the opposite side to the hypotenuse. With this information, let's find the adjacent side:

So, the opposite is 12 (ignore the negative for now) and the hypotenuse is 13. Therefore, we can use the Pythagorean Theorem:

a^2+b^2=c^2

Substitute 12 for a and 13 for c:

12^2+b^2=c^2

Now, solve for b to find the adjacent side. Square the values:

144+b^2=169

Subtract 144 from both sides:

b^2=25

Square root:

$b=\pm 5$

We can ignore the negative and just take the positive. While the answer is technically -5, we don't need to do that. So, our adjacent side is 5.

Therefore, with respect to angle θ, our opposite is 12, our adjacent is 5, and our hypotenuse is 13. With this, we can compute the other trig ratios. Let's start with the 3 main ones:

Sine:

$\sin(\theta)$

As given, this is -12/13. So:

$\sin(\theta)=-12/13$

Cosine:

$\cos(\theta)=adj/hyp$

Substitute 5 for the adjacent and 13 for the hypotenuse. So:

$\cos(\theta)=5/13$

And since our angle is in QIII, we add a negative:

$\cos(\theta)=-5/13$

Tangent:

$\tan(\theta)=opp/adj$

Substitute 12 for opposite and 5 for adjacent. So:

$\tan(\theta)=12/5$

And since our angle is in QIII, tangent stays positive.

To find the other three, simply flip the previous fractions:

$\csc(\theta)=-13/12\\\sec(\theta)=-13/5\\\cot(\theta)=5/12$

Answer from: Quest

the highest percentage for deaths in construction from highest to lowest is as follows: falls, struck by objects, electrocution, and caught-in/between. these four are collectively known as fatal four.

in the case of falls, the type that is responsible for the overall highest death in the category is falls from roofs.

Answer from: Quest

The answe may be c

Another question on Mathematics

Mathematics, 21.06.2019 22:10

Monitors manufactured by tsi electronics have life spans that have a normal distribution with a standard deviation of 1800 hours and a mean life span of 20,000 hours. if a monitor is selected at random, find the probability that the life span of the monitor will be more than 17,659 hours. round your answer to four decimal places.

Answers: 2

Answer

Mathematics, 22.06.2019 02:00

Taylor graphs the system below on her graphing calculator and decides that f(x)=g(x) at x=0, x=1, and x=3. provide taylor with some feedback that explains which part of her answer is incorrect and why it is incorrect. f(x)= 2x+1 g(x)= 2x^2+1

Answers: 2

Answer

Mathematics, 22.06.2019 04:20

Question 2 (essay worth 10 points) (03.02 mc) in δabc shown below, point a is at (0, 0), point b is at (x2, 0), point c is at (x1, y1), point d is at x sub 1 over 2, y sub 1 over 2, and point e is at the quantity of x sub 1 plus x sub 2 over 2, y sub 1 over 2: triangle abc is shown. point d lies on segment ac and point e lies on segment bc. a segment is drawn between points d and e. point a is at the origin. prove that segment de is parallel to segment ab.

Answers: 1

Answer

Mathematics, 22.06.2019 04:30

The function c(n) below relates the number of bushels of apples picked at a pick-your-own orchard to the final cost for the apples. it takes as input the number of bushels of apples picked after paying an entry fee to an orchard and returns as output and returns as output the cost of the apples (in dollars)c(n) = 15n + 30which equation below represents the inverse function n(c), which takes the cost of the apples as input and returns the number of bushels picked as output

Answers: 1

Answer

You know the right answer?

WILL GIVE BRAINIEST IF DONE IN 10 MINUTES If sinθ=−1213 and secθ<0 , what are the values of cosθ...

Questions