Question

Hey just came across this 6 mark question , help please??


(b) Solve, for 0 ≤ θ < 360°, the equation

2 tan2 θ + sec θ = 1,

giving your answers to 1 decimal place.

Answer 1

is that tangent squared?

Answer 2

Using sin^2x+cos^2x = 1 identity seems like a good start?

Answer 3

\[\sec \theta = 1 - 2\tan2\theta\]
square both sides
write sec^2 as 1 + tan^2
we get
4[\tan2\theta ^{2} = \tan ^{2}\]
sq root it
2 tan2(theta)=tantheta

Answer 4

2sin^2 x + cosx = cos^2x
This should result in a quadratic equation of cos x. Then, solve?

Answer 5

tan2theta = (2tan theta)/( 1+ tan^2)

Answer 6

hmmmm...that seems convoluted.

Answer 7

short way .. follow gt ..

Answer 8

sorry messed up in the equation writer

basically i converted the equation into tan(theta)

Answer 9

I messed up as well. good job GT

Answer 10

im getting theta = 0 or pi/3

Answer 11

but hey kinzan is that squared or 2theta ??

Answer 12

because i have solved for 2 theta and gt has solved taking squared

Answer 13

hey guys yeah it is tan^2

Answer 14

then follow gt 's answer

Answer 15

I did not give the answer. Rather the approach to convert the equation into a quadratic equation of cos(theta), which when solved will lead to the answer.

Answer 16

Add two to both sides first.

Answer 17

\[2\tan ^{2}\theta+2+\sec \theta=\]=3

Answer 18

Now factor 2 out of the first two terms:

Answer 19

\[2(\tan ^{2}\theta+1)+\sec \theta=3\]

Answer 20

Now substitute sec^2 for tan^2 + 1 and subtract 3 from both sides.

Answer 21

\[2\sec ^{2}\theta+\sec \theta-3=0\]

Answer 22

Now factor:

Answer 23

\[(2\sec \theta+3)(\sec \theta-1)=0\]

Answer 24

Can you get it from here?

Answer 25

\[\sec \theta=-1.5 or \sec \theta=1\]

Answer 26

theta = 2.3 radians or 0 radians

Answer 27

@Mertsj: Thanks ! But how do you work out theta= 2.3 radians on your calculator?
Do you use the rule : sec θ=1/cosθ ??

Answer 28

Yes

Answer 29

So cos theta = -2/3 or 1

Answer 30

you mean -3/2 right??

Answer 31

No. sec theta = -3/2 so cos theta = -2/3

Answer 32

So type -.666666666666666 into your calculator (which is set in radian mode) and hit the inverse cosine button.

Answer 33

Or if you calculator does fractions, type in -2/3 and push inverse cosine

Answer 34

i got 2.3?

Answer 35

theta = 2.3 radians or 0 radians

Answer 36

ohh sorry in degrees mode i got 131.8 which is correct!

Answer 37

yes, thanks! :D

Answer 38

Both are correct. 131.8 degrees or 2.3 radians. don't forget the 0 degrees or 0 radiana

Answer 39

thanks :)

Answer 40

yw