if sin x = 5/13 and tan x = -5/12 find the sec x?

Question

can you please show me the steps.thank you

Answer 1

Hi,

If the sine is positive, that would limit the angle to the first or second quadrants. If the tangent is negative, that would limit the angle to the second or fourth quadrants. For both to be true, it must be in the second quadrant.

If sin x = 5/13, then sin^-1(5/13) = 22.62°. this would be the reference angle so x is 180 - 22.62 or 157.38°.

The angle is 157.38° so sec 157.38° = 1/cos157.38° = -1.0833

I hope that helps!! :-)

Answer 2

since the tan is negative while sin is positive,
Then x is in the 2nd quarter ,
sec x = -13/12

Answer 3

Make a right angled triangle with the right angle on the right hand side, for convention.

Label this triangle ABC, where the angle on the left is A, the right angle 90* is B and C is above it, the third angle.

recalling sohcahtoa:
sinx=opp/hyp,
cosx=adj/hyp
tanx = opp/adj

sin x =5/13, gives your triangle the following length sides:
sideBC=5, the length of the 'opposite' side
sideAC=13 the hypotenuse.

tanx = -5/12
sideBC=5, as above, ignore the negative for one moment
sideAB=12 the base length in your triangle

We now know the lengths of all three sides of the triangle

AB=12
BC=5
AC=13

But in the tangent ratio, the adjacent must have been negative, because the opposite as seen in the sine ratio was positive 5.

This tells us that the triangle is in the second quadrant BTW.

secant is the same as one over cosine:

secx = 1/cosx

cosine is adjacent over hypotenuse.
cosx=-12/13 It is negative because the cosine 'is negative' in the second quadrant

now if secx = 1/cosx , then
secx= 1/(-12/13)

we take the reciprocal of -12/13 and get
secx= -(13/12)

Answer 4

-13/2

Answer 5

Well, sec(x) = tan(x)/sin(x).

You were given the values of tan(x) and sin(x), right?

We plug and chug.

sex (x) = -5/12 divided by 5/13

We have created a complex fraction.

When we divide fractions, we FLIP OVER the right side fraction and then multiply.

Recall from primary school?

sec(x) = -5/12 times 13/5

sec(x) = -13/12

Did you follow?

Answer 6

sin=opposite/hypotenuse =5/13
tan=opposite /adjacent=-5/12
opp=5, hypot=13, adj=-12
secant= hypot/adj, =13/-12, or -13/12

Answer 7

This one is a litte easy to answer, since the numbers look familiar.

We're dealing with a right triangle with legs 5,12, and hypotenuse 13—a Pythagorean triple.

We also know that the only place tan x is negative and sin x is positive is in the II quadrant, so we know that cos x is negative. Since sec x = 1/cos x, and cos x = adjacent/hypotenuse = -12/13,

sec x = -13/12

Answer 8

a positive sine and a negative tan, tells us that x is in the 2nd quadrant, so the secant will be negative (1/cos). Since cos is -12/13, sec x = -13/12

that's it! :)

Answer 9

tan(x) = sin(x)/cos(x)
cos(x) = sin(x)/tan(x)
sec(x) = 1/cos(x) = tan(x)/sin(x)

sec(x) = (-5/12) / (5/13)
= -13/12

Answer 10

x is in 2 nd quadrant
sec x = 1 / cos x
sec x = 1 / (- 12/13)
sec x = - 13 / 12