{"id":20118,"date":"2022-12-17T08:54:37","date_gmt":"2022-12-17T08:54:37","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=10414"},"modified":"2022-12-17T08:54:37","modified_gmt":"2022-12-17T08:54:37","slug":"sine-cosine-and-tangent","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/12\/17\/sine-cosine-and-tangent\/","title":{"rendered":"Sine, Cosine and Tangent"},"content":{"rendered":"\n

The main functions in trigonometry are\u00a0Sine, Cosine and Tangent<\/p>\n\n\n\n

They are simply one side of a right-angled triangle divided by another.<\/p>\n\n\n\n

For any angle “\u03b8<\/em><\/strong>“:<\/p>\n\n\n\n

\"sin=opposite\/hypotenuse<\/figure>\n\n\n\n

(Sine, Cosine and Tangent are often abbreviated to sin, cos and tan.)<\/em><\/p>\n\n\n\n

Example: What is the sine of 35\u00b0?<\/h3>\n\n\n\n
\"triangle<\/figure>\n\n\n\n

Using this triangle (lengths are only to one decimal place):<\/p>\n\n\n\n

sin(35\u00b0) = Opposite<\/em>Hypotenuse<\/strong> = 2.8<\/em>4.9<\/strong> = 0.57…<\/strong><\/p>\n\n\n\n

The triangle could be larger, smaller or turned around, but that angle will always have that ratio<\/strong>.<\/p>\n\n\n\n

Calculators have sin, cos and tan to help us, so let’s see how to use them:<\/p>\n\n\n\n

 \"right<\/p>\n\n\n\n

Example: How Tall is The Tree?<\/h3>\n\n\n\n

We can’t reach the top of the tree, so we walk away and measure an angle (using a protractor) and distance (using a laser):<\/p>\n\n\n\n

    \n
  • We know the Hypotenuse<\/strong><\/li>\n\n\n\n
  • And we want to know the Opposite<\/strong><\/li>\n<\/ul>\n\n\n\n

    Sine<\/strong> is the ratio of Opposite \/ Hypotenuse<\/strong>:<\/p>\n\n\n\n

    sin(45\u00b0) = Opposite<\/em>Hypotenuse<\/strong><\/p>\n\n\n\n

    \"calculator-sin-cos-tan\"\/<\/figure>\n\n\n\n

    Get a calculator, type in “45”, then the “sin” key:<\/p>\n\n\n\n

    sin(45\u00b0) = 0.7071…<\/strong><\/p>\n\n\n\n

    What does the 0.7071…<\/strong> mean? It is the ratio of the side lengths, so the Opposite is about 0.7071<\/em> times as long as the Hypotenuse.<\/p>\n\n\n\n

    We can now put 0.7071…<\/strong> in place of sin(45\u00b0):<\/p>\n\n\n\n

    0.7071…<\/strong> = Opposite<\/em>Hypotenuse<\/strong><\/p>\n\n\n\n

    And we also know the hypotenuse is 20<\/strong>:<\/p>\n\n\n\n

    0.7071… = Opposite<\/em>20<\/strong><\/p>\n\n\n\n

    To solve, first multiply both sides by 20:<\/p>\n\n\n\n

    20 \u00d7 0.7071… = Opposite<\/p>\n\n\n\n

    Finally:<\/p>\n\n\n\n

    Opposite = 14.14m<\/strong> (to 2 decimals)When you gain more experience you can do it quickly like this:<\/p>\n\n\n\n

    \"right<\/figure>\n\n\n\n

    Example: How Tall is The Tree?<\/h3>\n\n\n\n

    Start with:sin(45\u00b0) = Opposite<\/em>Hypotenuse<\/strong><\/p>\n\n\n\n

    We know:0.7071… = Opposite<\/em>20<\/strong><\/p>\n\n\n\n

    Swap sides:Opposite<\/em>20<\/strong> = 0.7071…<\/p>\n\n\n\n

    Multiply both sides by 20<\/strong>:Opposite = 0.7071… \u00d7 20<\/p>\n\n\n\n

    Calculate:Opposite = 14.14<\/strong>
    (to 2 decimals)<\/p>\n\n\n\n

    The tree is 14.14m tall<\/p>\n","protected":false},"excerpt":{"rendered":"

    The main functions in trigonometry are\u00a0Sine, Cosine and Tangent They are simply one side of a right-angled triangle divided by another. For any angle “\u03b8“: (Sine, Cosine and Tangent are often abbreviated to sin, cos and tan.) Example: What is the sine of 35\u00b0? Using this triangle (lengths are only to one decimal place): sin(35\u00b0) = OppositeHypotenuse = 2.84.9 = 0.57… […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[333],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/20118"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=20118"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/20118\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=20118"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=20118"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=20118"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}