Question

the expression

Answer 1

Formula: \(\cos^2\theta+\sin^2\theta=1\)
Derived formulas: \(\cos^2\theta=1-\sin^2\theta\); \(\sin^2\theta=1-\cos^2\theta\)

Answer 2

\[\frac{\color{green}{\sin^2\theta+\cos^2\theta}}{\color{blue}{1-\sin^2\theta}}=\frac{\color{green}1}{\color{blue}{\cos^2\theta}}(=\sec^2\theta)\]

Answer 3

So the answer isn't cos^2 theta

Answer 4

my mistake i got it thanks. are you a math teacher?

Answer 5

No, I'm a grade 9 student

Answer 6

wow you are a smart kid

Answer 7

thank you

Answer 8

how do u know trig well

Answer 9

I learnt it years ago; my dad taught me all those stuffs

Answer 10

wow

Answer 11

could you answer one more question plz find all the values of theta in the interval \[0<\theta < 360\] that satisfy the equation \[3 \cos 2\theta + 2 \sin \theta +1=0 \]
round answers to nearest hundredth of the degree

Answer 12

@kc_kennylau plz

Answer 13

Use a formula to convert \(\cos2\theta\) first

Answer 14

Basic formulas:
\[\sin^2\theta+\cos^2\theta=1\]\[\tan\theta=\frac{\sin\theta}{\cos\theta}\]Double angle formulas:\[\sin2\theta=2\sin\theta\cos\theta\]\[\cos2\theta=\cos^2\theta-\sin^2\theta\]

Answer 15

Use the last formula first

Answer 16

\[\begin{array}{cl}
&3\color{green}{\cos2\theta}+2\sin\theta+1\\
=&3\color{green}{(\cos^2\theta-\sin^2\theta)}+2\sin\theta+1\\
=&3\cos^2\theta-3\sin^2\theta+2\sin\theta+1\\
=&3\color{blue}{\cos^2\theta}-3\sin^2\theta+2\sin\theta+1\\
=&3\color{blue}{(1-\sin^2\theta)}-3\sin^2\theta+2\sin\theta+1\\
=&3-3\sin^2\theta-3\sin^2\theta+2\sin\theta+1\\
=&-6\sin^2\theta+2\sin\theta+4
\end{array}\]

Answer 17

Now it's transformed into a quadratic equation