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  2. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    The triangle shaded blue illustrates the identity + ⁡ = ⁡, and the red triangle shows that ⁡ + = ⁡. The basic relationship between the sine and cosine is given by the Pythagorean identity: sin 2 ⁡ θ + cos 2 ⁡ θ = 1 , {\displaystyle \sin ^{2}\theta +\cos ^{2}\theta =1,}

  3. Proofs of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/Proofs_of_trigonometric...

    The area of triangle OCD is CD/2, or tan(θ)/2. Since triangle OAD lies completely inside the sector, which in turn lies completely inside triangle OCD, we have ⁡ < < ⁡. This geometric argument relies on definitions of arc length and area, which act as assumptions, so it is rather a condition imposed in construction of trigonometric ...

  4. Pythagorean trigonometric identity - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_trigonometric...

    Similar right triangles illustrating the tangent and secant trigonometric functions Trigonometric functions and their reciprocals on the unit circle. The Pythagorean theorem applied to the blue triangle shows the identity 1 + cot 2 θ = csc 2 θ, and applied to the red triangle shows that 1 + tan 2 θ = sec 2 θ.

  5. Area of a triangle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_triangle

    The area of a triangle can be demonstrated, for example by means of the congruence of triangles, as half of the area of a parallelogram that has the same base length and height. A graphic derivation of the formula T = h 2 b {\displaystyle T={\frac {h}{2}}b} that avoids the usual procedure of doubling the area of the triangle and then halving it.

  6. Minoxidil 10% and 15%: Is High Strength More Effective? - AOL

    www.aol.com/minoxidil-10-15-high-strength...

    At 2% and 5%, minoxidil is FDA-approved to treat androgenic alopecia (male pattern baldness and female pattern hair loss). It’s also used off-label to treat other types of hair loss, including ...

  7. The top 7 mental health challenges of the holidays and how to ...

    www.aol.com/top-7-mental-health-challenges...

    2. Overwhelm and Burnout. ... A 2021 survey found that 36% of people who have experienced significant loss report that the holidays as one of the most difficult times of the year.

  8. Exact trigonometric values - Wikipedia

    en.wikipedia.org/wiki/Exact_trigonometric_values

    In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained. By symmetry, the bisected side is half of the side of the equilateral triangle, so one concludes sin ⁡ ( 30 ∘ ) = 1 / 2 {\displaystyle \sin(30^{\circ ...

  9. Israeli military kills four doctors in raid on Kamal Adwan ...

    www.aol.com/israeli-military-kills-four-doctors...

    Four doctors were killed at the Kamal Adwan Hospital in besieged northern Gaza on Friday, after Israeli forces stormed the compound, killing and injuring dozens of people in areas surrounding the ...

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