find sec C and sin C if tan c= -1 and cos C > 0?

Question

i need help understanding this ..i nkow x over r and r is aways psitive or and opp ver hypoth...?????????some one help

Answer 1

I know that without any computation
sec C = sqrt(2)
sin C = - sqrt(2) / 2
C = -45 degrees or 315 degrees (bonus for you)

Answer 2

Think in terms of a right angled triangle with A and B as sides and C as hypotenuse.

tan c = opp. side/adj. side = -1 ; hence A/B = -1 i.e A = -B;

This means that A & B are equal in length but in opposite quadrants. If two sides of a right angled triangle are equal then the hypotenuse is sqrt(2). So C = sqrt(2).

The triangle is an isoceles right triangle because A = B hence the 2 angles are 45 degrees each. ( 3 rd angle is 90 degrees)

sine 45 = 1/sqrt(2) = cos 45.
sec 45 = 1/cos 45 = sqrt(2)

You can also use trigonometry to solve it as shown by many other answerers. For simplicity of understanding think of an isoceles right angle triangle.

Answer 3

To start with, tan c = sin c / cos c, so if we want tan c = -1, we need to find an angle where cos c and sin c are equal in magnitude but opposite in sign. The only two places that happens are at c = 135º (cos c = -1/√2 and sin c = +1/√2) and c = 315º (cos c = +1/√2 and sin c = -1/√2), and since we want cos c > 0, 315º is the only possible solution.

At 315º, sin c = -1/√2, and sec c = 1/cos c = √2.

Hope that helps!

Answer 4

Use the fact that tan C = (sin C) / (cos C)

if tan C = -1, then sin C = - cos C

Moreover, (sin C)^2 + (cos C)^2 = 1

Because these squares are equal, they must be 1/2, and therefore

sin C and cos C are +/- sqrt (1/2)

You know cos C > 0, so

cos C = + sqrt (1/2)

sec C = 1 / cos C = 1/sqrt(1/2) = + sqrt 2

sin C = - cos C [see above] = - sqrt (1/2)

Answer 5

well,

if you know tan c = -1, then you know c... however, all trigonometric functions are double-valued... which means that there are two values for c that will give you tan c = -1...

for tan c = -1 these are: c = -45, 135 degrees...

for this we know -45 is in the 4th quadrant... which means the cosine (adjacent/hypoteneuse) will be a positive/positive therefore cos c (or -45 or 315 degrees) will be greater than zero...

so c = -45 or 315 degrees (-pi/4 or 7pi/4 in rads)

therefore,

sin c = sin 315 = -sqrt(2)/2 or -1/sqrt(2)...

and sec c = sec 315 = 1/cos(315) = sqrt(2)

Answer 6

What's the problem
Tan c=-1
1+tan^2x=sec^2x
so sec^2x=2
sec=+-sqrt(2)
sec c=+sqrt(2)=1.4
cos c=1/sqrt(2)=0.71428571428571428571428571428571
so sinc= -sqrt(1-cos^2c)
Find the vlaues self
remember sin c would be -ve

Answer 7

sinC = - 0.5*sqrt(2)
secC = sqrt(2)

C equals -45 degrees or -pi/4

Answer 8

tanC=opp.side/adj.side=-1/1
hypotenuse=(2)^1/2
cosC>0 so seC>0=
sec=hyp/adj=(2)^1/2/1
and sinC=opp.side/hyp=-1/(2)^1/2