For those who don't know part 1 (Determinants)

Algebra Level 1

X = ∣ − sin ⁡ θ cos ⁡ θ − cos ⁡ θ − sin ⁡ θ ∣ X=\begin{vmatrix} -\sin { \theta } & \cos { \theta } \\ -\cos { \theta } & -\sin { \theta } \end{vmatrix} .

Find the value of determinant ( X X ).

If you don't know how to expand determinants, look at this note WIKI .


The answer is 1.

Abdulrahman El Shafei by Abdulrahman El Shafei , 23, Egypt

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4 solutions

If you don't know how to expand determinants, look at this WIKI .

X = ∣ − sin ⁡ θ cos ⁡ θ − cos ⁡ θ − sin ⁡ θ ∣ X = sin ⁡ 2 θ + cos ⁡ 2 θ = 1 X=\begin{vmatrix} -\sin { \theta } & \cos { \theta } \\ -\cos { \theta } & -\sin { \theta } \end{vmatrix}\\ X=\sin ^{ 2 }{ \theta } +\cos ^{ 2 }{ \theta } =\boxed { 1 }

27 Helpful 0 Interesting 0 Brilliant 0 Confused

Fortunately, I read the title, but please put "what's the value of det(X)" rather than "what's the value of X"

Curtis Clement - 6 years, 5 months ago
Muhammad Pasha
Jan 18, 2015

X = (-sin theta)(-sin theta) - (-cos theta)(cos theta)

X = sin ^2 theta + cos^2 theta

We know that sin ^2 theta + cos^2 theta = 1

So X = 1

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Relevant wiki: Determinants

1 Helpful 0 Interesting 0 Brilliant 0 Confused

This solution is too big, good for the people with eyesight problems.

A Former Brilliant Member - 3 years, 6 months ago
Nehem Tudu
Jan 9, 2015

(sin theta)^2+(cos theta)^2=1

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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