Question

If Cos theta= 7/25 find the value of all T-ratios of theta​

Answer 1

AnsWer :

• Sin theta = 24 / 25.
• Cos theta = 7 / 25.
• Tan theta = 24 / 7.
• Cosec theta = 25 / 24.
• Sec theta = 25 / 7.
• Cot theta = 7 / 24.

SolutioN :

We know,

• Sin²A + Cos²A = 1.

$\tt \dagger \: \: \: \: \: {sin}^{2} \theta + {cos}^{2} \theta = 1.$

$\tt \longmapsto {sin}^{2} \theta + { \bigg(\dfrac{7}{25} \bigg)}^{2} = 1.$

$\tt \longmapsto {sin}^{2} \theta + \dfrac{49}{625} = 1.$

$\tt \longmapsto {sin}^{2} \theta = 1 - { \dfrac{49}{625}}$

$\tt \longmapsto {sin}^{2} \theta = { \dfrac{625 - 49}{625}}$

$\tt \longmapsto {sin}^{2} \theta = { \dfrac{576}{625}}$

$\tt \longmapsto {sin}\theta = \sqrt{{ \dfrac{576}{625}}}$

$\tt \longmapsto {sin}\theta = \pm { \dfrac{24}{25}}$

Now, We have.

$\tt \dagger \: \: \: \: \: Sin \theta = \dfrac{Perpendicular }{Hypotenuse }.$

$\tt \dagger \: \: \: \: \: Cos \theta = \dfrac{Base }{Hypotenuse }.$

$\tt \dagger \: \: \: \: \: tan\theta = \dfrac{Perpendicular }{Base }.$

$\tt \dagger \: \: \: \: \: Cosec \theta = \dfrac{Hypotenuse}{Perpendicular }.$

$\tt \dagger \: \: \: \: \: Sec \theta = \dfrac{Hypotenuse }{Base }.$

$\tt \dagger \: \: \: \: \: Cot\theta = \dfrac{Base }{Perpendicular }.$

• Sin theta = 24 / 25.
• Cos theta = 7 / 25.
• Tan theta = 24 / 7.
• Cosec theta = 25 / 24.
• Sec theta = 25 / 7.
• Cot theta = 7 / 24.

Answer 2

Answer

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