Is the trigonometry we are doing correct?

I am considering \[\cos\theta=\sec\theta\]then \[\cos\theta=\frac{1}{\cos\theta}\] \[=>\cos^2\theta=1\] \[=>\cos\theta=1\] \[=>\theta=0^\circ\]here \[\sin\theta=\sin 0^\circ=0.\] the next way again consider \[\cos\theta=\sec\theta\] \[=>\frac{adj}{hyp}=\frac{hyp}{adj}\] \[=>\frac{adj^2}{hyp^2}=1\] \[=>\cos^2\theta=1\] \[=>\cos\theta=-1\] nothing too interesting here

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

Note: $\cos ^2 \theta = 1 \not \Rightarrow \cos \theta = 1$ . Do you see why?

Calvin Lin Staff - 6 years, 4 months ago

why staff iam sending the sqare to that side so $\cos\theta=1$ hmmm.. ttooo simple concept

sudoku subbu - 6 years, 4 months ago

If $x^2 = 1$ , is $x = 1$ the only solution?

Calvin Lin Staff - 6 years, 4 months ago

@Calvin Lin – ya ya i understand your concept if $x^2=1$ then x may be -1 or +1 thanks calvin i'll change

sudoku subbu - 6 years, 4 months ago

@Sudoku Subbu – Right, that is a very common mistake made when trying to solve such equations.

The best approach would be to say $0 = x^2 - 1 = (x-1)(x+1)$ and hence $x = 1, -1$ .

Calvin Lin Staff - 6 years, 4 months ago

@Calvin Lin – thanks for your help visit my other notes and reply if there is any mistake

sudoku subbu - 6 years, 4 months ago

@Sudoku Subbu – We can't say "concept" when we talk about "Fundamental theorem of algebra".

Andi Popescu - 6 years, 3 months ago

Another thing... you don't just consider the first quadrant angle.. Consider also its coterminal angles..

John Ashley Capellan - 6 years, 4 months ago

Remember the Pythagorean Identity: $\sin^2{\theta}+\cos^2{\theta}=1$ If $\cos^2{\theta}=1$ , this implies that: $\sin^2{\theta}=0 \\ \sin{\theta}=0$ ¿For what angles is this true? For any angle of the form $\theta=n\pi$ As can be easily verified seeing any graph of the sine function.

Ricardo Adán Cortés Martín - 6 years, 4 months ago

boss what r u trying to tel??

SARAN .P.S - 5 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$